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Sun Y, Hu M, Deng Y, Lv JP. Extraordinary-log Universality of Critical Phenomena in Plane Defects. PHYSICAL REVIEW LETTERS 2023; 131:207101. [PMID: 38039462 DOI: 10.1103/physrevlett.131.207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Revised: 08/24/2023] [Accepted: 10/13/2023] [Indexed: 12/03/2023]
Abstract
The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale Monte Carlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O(n) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for n=2, the critical exponent q[over ^] of two-point correlation and the renormalization-group parameter α of helicity modulus conform to the scaling relation q[over ^]=(n-1)/(2πα), whereas the results for n≥3 violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.
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Affiliation(s)
- Yanan Sun
- Department of Physics, Anhui Key Laboratory of Optoelectric Materials Science and Technology, Key Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Normal University, Wuhu, Anhui 241000, China
| | - Minghui Hu
- Department of Physics, Anhui Key Laboratory of Optoelectric Materials Science and Technology, Key Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Normal University, Wuhu, Anhui 241000, China
| | - Youjin Deng
- National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Ping Lv
- Department of Physics, Anhui Key Laboratory of Optoelectric Materials Science and Technology, Key Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Normal University, Wuhu, Anhui 241000, China
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2
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Rakala G, Damle K, Dhar D. Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets. Phys Rev E 2021; 103:062101. [PMID: 34271608 DOI: 10.1103/physreve.103.062101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent θ and the dynamical exponent z of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength η_{m}, where η_{m} is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, z=(2-η_{m})/(1-θ), that allows us to express the dynamical exponent z(η_{m}) of this process in terms of its persistence exponent θ(η_{m}). Our measurements of z(η_{m}) and θ(η_{m}) are consistent with this relation over a range of values of the universal equilibrium exponent η_{m} and yield subdiffusive (z>2) values of z in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.
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Affiliation(s)
- Geet Rakala
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0412, Japan
| | - Kedar Damle
- Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India
| | - Deepak Dhar
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
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3
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Jiang J, Wang ZG. Improved local lattice Monte Carlo simulation for charged systems. J Chem Phys 2018; 148:114105. [DOI: 10.1063/1.5023491] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Jiang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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4
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Álvarez Zúñiga JP, Luitz DJ, Lemarié G, Laflorencie N. Critical properties of the superfluid-bose-glass transition in two dimensions. PHYSICAL REVIEW LETTERS 2015; 114:155301. [PMID: 25933319 DOI: 10.1103/physrevlett.114.155301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5). Our results give the following estimates for the critical exponents: z=1.85(15), ν=1.20(12), η=-0.40(15). Furthermore, the probability distribution of the SF response P(lnρSF) displays striking differences across the transition: while it narrows with increasing system sizes L in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point P(lnρSF+zlnL) is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.
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Affiliation(s)
| | - David J Luitz
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France
| | - Gabriel Lemarié
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France
| | - Nicolas Laflorencie
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France
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5
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Wang Y, Guo W, Sandvik AW. Anomalous quantum glass of bosons in a random potential in two dimensions. PHYSICAL REVIEW LETTERS 2015; 114:105303. [PMID: 25815942 DOI: 10.1103/physrevlett.114.105303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Indexed: 06/04/2023]
Abstract
We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.
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Affiliation(s)
- Yancheng Wang
- Department of Physics, Beijing Normal University, Beijing 100875, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenan Guo
- Department of Physics, Beijing Normal University, Beijing 100875, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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6
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Deschner A, Sørensen ES. Valence-bond quantum Monte Carlo algorithms defined on trees. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033304. [PMID: 25314561 DOI: 10.1103/physreve.90.033304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Indexed: 06/04/2023]
Abstract
We present a class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a projective T=0 Monte Carlo method based on sampling of a set of operator strings that can be viewed as forming a treelike structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator string. In quite general terms, we derive a set of equations whose solutions correspond to a whole class of algorithms. As specific examples of this class of algorithms, we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree, and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.
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Affiliation(s)
- Andreas Deschner
- Department of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1
| | - Erik S Sørensen
- Department of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1
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7
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Carleo G, Boéris G, Holzmann M, Sanchez-Palencia L. Universal superfluid transition and transport properties of two-dimensional dirty bosons. PHYSICAL REVIEW LETTERS 2013; 111:050406. [PMID: 23952374 DOI: 10.1103/physrevlett.111.050406] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Indexed: 06/02/2023]
Abstract
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.
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Affiliation(s)
- Giuseppe Carleo
- Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ Paris Sud 11, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France
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9
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Gazit S, Podolsky D, Auerbach A. Fate of the Higgs mode near quantum criticality. PHYSICAL REVIEW LETTERS 2013; 110:140401. [PMID: 25166962 DOI: 10.1103/physrevlett.110.140401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2012] [Indexed: 06/03/2023]
Abstract
We study a relativistic O(N) model near the quantum critical point in 2 + 1 dimensions for N = 2 and N = 3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a well-defined peak associated with the Higgs mode arbitrarily close to the critical point. The peak fidelity and the amplitude ratio between the critical energy scales on both sides of the transition are determined.
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Affiliation(s)
- Snir Gazit
- Physics Department, Technion, 32000 Haifa, Israel
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10
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Meier H, Wallin M. Quantum critical dynamics simulation of dirty boson systems. PHYSICAL REVIEW LETTERS 2012; 108:055701. [PMID: 22400943 DOI: 10.1103/physrevlett.108.055701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2011] [Indexed: 05/31/2023]
Abstract
Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied.
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Affiliation(s)
- Hannes Meier
- Department of Theoretical Physics, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
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11
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Thompson D, Rottler J. Local Monte Carlo for electrostatics in anisotropic and nonperiodic geometries. J Chem Phys 2008; 128:214102. [DOI: 10.1063/1.2918361] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Pasichnyk I, Everaers R, Maggs AC. Simulating Van Der Waals Interactions in Water/Hydrocarbon-Based Complex Fluids. J Phys Chem B 2008; 112:1761-4. [DOI: 10.1021/jp077401m] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- I. Pasichnyk
- Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D-01187 Dresden, Germany
| | - R. Everaers
- Université de Lyon, Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672, 46 allée d'Italie, 69364 Lyon Cedex 07, France
| | - A. C. Maggs
- Laboratoire de Physico-Chimie Théorique, UMR CNRS−ESPCI 7083, 10 rue Vauquelin, F-75231 Paris Cedex 05, France
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13
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Karttunen M, Rottler J, Vattulainen I, Sagui C. Chapter 2 Electrostatics in Biomolecular Simulations: Where Are We Now and Where Are We Heading? CURRENT TOPICS IN MEMBRANES 2008. [DOI: 10.1016/s1063-5823(08)00002-1] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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14
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Cha MC, Lee JW. Finite-temperature phase transitions in a two-dimensional boson Hubbard model. PHYSICAL REVIEW LETTERS 2007; 98:266406. [PMID: 17678114 DOI: 10.1103/physrevlett.98.266406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2007] [Indexed: 05/16/2023]
Abstract
We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of a quantum rotor model and construct the corresponding phase diagram. Compressibility shows a thermally activated gapped behavior in the insulating regime. Finite-size scaling of the superfluid stiffness clearly shows the nature of the Kosterlitz-Thouless transition. The transition temperature T(c) confirms a scaling relation T(c) proportional, rho(0)(x), with x=1.0. Some evidence of anomalous quantum behavior at low temperatures is presented.
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Affiliation(s)
- Min-Chul Cha
- Department of Applied Physics, Hanyang University, Ansan 426-791, Korea
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15
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Weichman PB, Mukhopadhyay R. Critical dynamics of the dirty boson problem: revisiting the equality z=d. PHYSICAL REVIEW LETTERS 2007; 98:245701. [PMID: 17677974 DOI: 10.1103/physrevlett.98.245701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2007] [Indexed: 05/16/2023]
Abstract
It is shown that previous arguments, leading to the equality z=d for the dynamical exponent describing the Bose glass to superfluid transition in d dimensions, may break down, as apparently seen in recent simulations. The key observation is that the major contribution to the compressibility, which remains finite through the transition and was predicted to scale as kappa approximately |delta|((d-z)nu) (where delta is the deviation from criticality and nu is the correlation length exponent) comes from the analytic, not the singular part of the free energy, and is not restricted by any conventional scaling hypothesis.
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Affiliation(s)
- Peter B Weichman
- BAE Systems, Advanced Information Technologies, 6 New England Executive Park, Burlington, Massachusetts 01803, USA
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16
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Priyadarshee A, Chandrasekharan S, Lee JW, Baranger HU. Quantum phase transitions of hard-core bosons in background potentials. PHYSICAL REVIEW LETTERS 2006; 97:115703. [PMID: 17025902 DOI: 10.1103/physrevlett.97.115703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2006] [Indexed: 05/12/2023]
Abstract
We study the zero temperature phase diagram of hard-core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid (at small potential) to a normal phase (at large potential), but with different universality classes. As expected, the staggered case belongs to the XY universality, while the uniform potential induces a mean field transition. The disorder driven transition is clearly different from both; in particular, we find z approximately 1.4, nu approximately 1, and beta approximately 0.6.
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Affiliation(s)
- Anand Priyadarshee
- Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708-0305, USA
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17
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Maggs AC, Everaers R. Simulating nanoscale dielectric response. PHYSICAL REVIEW LETTERS 2006; 96:230603. [PMID: 16803362 DOI: 10.1103/physrevlett.96.230603] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2005] [Indexed: 05/10/2023]
Abstract
We introduce a constrained energy functional to describe dielectric response. We demonstrate that the local functional is a generalization of the long-ranged Marcus energy. Our reformulation is used to implement a cluster Monte Carlo algorithm for the simulation of dielectric media. The algorithm avoids solving the Poisson equation and remains efficient in the presence of spatial heterogeneity, nonlinearity, and scale dependent dielectric properties.
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Affiliation(s)
- A C Maggs
- Laboratoire de Physico-Chime Théorique, UMR CNRS-ESPCI 7083, 10 rue Vauquelin, 75231 Paris Cedex 05, France
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18
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Duncan A, Sedgewick RD. Accelerated multiboson algorithm for Coulomb gases with dynamical dielectric effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066711. [PMID: 16907027 DOI: 10.1103/physreve.73.066711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2006] [Indexed: 05/11/2023]
Abstract
A recent reformulation [Phys. Rev. E 73, 016705 (2006)] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite-temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a spatial lattice by including additional bosonic fields. For large systems, the Monte Carlo algorithm proposed in the above-cited work becomes inefficient due to a low acceptance rate for particle moves in a fixed background multiboson field. We show here how this problem can be circumvented by use of a coupled particle-multiboson update procedure that improves acceptance rates on large lattices by orders of magnitude. The method is tested on a one-component plasma with neutral dielectric particles for a variety of system sizes.
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Affiliation(s)
- A Duncan
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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19
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Smakov J, Sørensen E. Universal scaling of the conductivity at the superfluid-insulator phase transition. PHYSICAL REVIEW LETTERS 2005; 95:180603. [PMID: 16383887 DOI: 10.1103/physrevlett.95.180603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2005] [Indexed: 05/05/2023]
Abstract
The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from omega k scaling of the conductivity towards omega k/T scaling at low Matsubara frequencies omega k. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with omega/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be sigma* = 0.45(5)Q2/h, distinct from previous estimates in the T = 0, omega/T >> 1 limit.
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Affiliation(s)
- Jurij Smakov
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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20
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Wang JS. Worm algorithm for two-dimensional spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:036706. [PMID: 16241613 DOI: 10.1103/physreve.72.036706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/05/2023]
Abstract
A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is efficient, particularly if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c approximately T-2 exp [-2J/( kB T) ] , where T is temperature and J is coupling constant, for the two-dimensional +/- J spin glass.
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Affiliation(s)
- Jian-Sheng Wang
- Singapore-MIT Alliance and Department of Computational Science, National University of Singapore, Singapore 117543, Republic of Singapore
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21
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Balabanyan KG, Prokof'ev N, Svistunov B. Superfluid-insulator transition in a commensurate one-dimensional bosonic system with off-diagonal disorder. PHYSICAL REVIEW LETTERS 2005; 95:055701. [PMID: 16090888 DOI: 10.1103/physrevlett.95.055701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2004] [Revised: 05/03/2005] [Indexed: 05/03/2023]
Abstract
We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.
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Affiliation(s)
- Karén G Balabanyan
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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22
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Burovski E, Kozik E, Kuklov A, Prokof'ev N, Svistunov B. Superfluid interfaces in quantum solids. PHYSICAL REVIEW LETTERS 2005; 94:165301. [PMID: 15904238 DOI: 10.1103/physrevlett.94.165301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2004] [Indexed: 05/02/2023]
Abstract
One scenario for the nonclassical moment of inertia of solid 4He discovered by Kim and Chan [Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal--the checkerboard lattice solid--we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U(1) universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.
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Affiliation(s)
- Evgeni Burovski
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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23
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Vestergren A, Lidmar J, Wallin M. Generalized anisotropic scaling theory and the transverse meissner transition. PHYSICAL REVIEW LETTERS 2005; 94:087002. [PMID: 15783921 DOI: 10.1103/physrevlett.94.087002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2004] [Indexed: 05/24/2023]
Abstract
We consider a depinning transition in vortex systems with columnar disorder and tilted applied magnetic fields. From scaling arguments and Monte Carlo simulations, we find that this transverse Meissner transition is governed by a fixed point which is anisotropic in all three directions. This generalization of conventional anisotropic scaling means that the correlation length in different directions diverges with different rates, and we derive exact results for the anisotropy exponents. We make predictions which can be tested in experiments on superconductors with columnar disorder.
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Affiliation(s)
- Anders Vestergren
- Condensed Matter Theory, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
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24
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Alet F, Wessel S, Troyer M. Generalized directed loop method for quantum Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036706. [PMID: 15903632 DOI: 10.1103/physreve.71.036706] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2004] [Revised: 12/22/2004] [Indexed: 05/02/2023]
Abstract
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the nonuniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however, we find that the optimal strategy depends not only on the model parameters but also on the observable of interest.
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Affiliation(s)
- Fabien Alet
- Theoretische Physik, ETH Zürich, Switzerland
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Kuklov A, Prokof'ev N, Svistunov B. Weak first-order superfluid-solid quantum phase transitions. PHYSICAL REVIEW LETTERS 2004; 93:230402. [PMID: 15601129 DOI: 10.1103/physrevlett.93.230402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2004] [Indexed: 05/24/2023]
Abstract
We study superfluid-solid zero-temperature transitions in two-dimensional lattice boson-spin models using worm-algorithm Monte Carlo simulations. We observe that such transitions are typically first order with the exception of special high-symmetry points which require fine-tuning in the Hamiltonian parameter space. We present evidence that the superfluid-checkerboard solid and superfluid-valence-bond solid transitions at half-integer filling factor are extremely weak first-order transitions and in small systems can be confused with continuous or high-symmetry points.
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Affiliation(s)
- Anatoly Kuklov
- Department of Engineering Science and Physics, The College of Staten Island, City University of New York, Staten Island, New York 10314, USA
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Hitchcock P, Sørensen ES, Alet F. Dual geometric worm algorithm for two-dimensional discrete classical lattice models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016702. [PMID: 15324199 DOI: 10.1103/physreve.70.016702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2003] [Indexed: 05/24/2023]
Abstract
We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof'ev and Svistunov [Phys. Rev. Lett. 87, 160601 (2001)]]. The algorithm is defined on the dual lattice and is formulated in terms of bond variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be "directed" by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.
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Affiliation(s)
- Peter Hitchcock
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1.
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Kuklov A, Prokof'ev N, Svistunov B. Commensurate two-component bosons in an optical lattice: ground state phase diagram. PHYSICAL REVIEW LETTERS 2004; 92:050402. [PMID: 14995288 DOI: 10.1103/physrevlett.92.050402] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2003] [Indexed: 05/24/2023]
Abstract
Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable super-fluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a d-dimensional quantum system onto a (d+1)-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from the MF predictions.
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Affiliation(s)
- Anatoly Kuklov
- Department of Engineering Science and Physics, The College of Staten Island, City University of New York, Staten Island, New York 10314, USA
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Kuklov A, Prokof'ev N, Svistunov B. Superfluid-superfluid phase transitions in a two-component Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2004; 92:030403. [PMID: 14753853 DOI: 10.1103/physrevlett.92.030403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2003] [Indexed: 05/24/2023]
Abstract
Depending on the Hamiltonian parameters, two-component bosons in an optical lattice can form at least three different superfluid phases in which both components participate in the superflow: a (strongly interacting) mixture of two miscible superfluids (2SF), a paired superfluid (PSF) vacuum, and (at a commensurate total filling factor) the super-counter-fluid (SCF) state. We study the universal properties of the 2SF-PSF and 2SF-SCF quantum phase transitions and show that (i) they can be mapped onto each other and (ii) their universality class is identical to the (d+1)-dimensional normal-superfluid transition in a single-component liquid. The finite-temperature 2SF-PSF(SCF) transitions and the topological properties of 2SF-PSF(SCF) interfaces are also discussed.
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Affiliation(s)
- Anatoly Kuklov
- Department of Engineering Science and Physics, The College of Staten Island, City University of New York, Staten Island, New York 10314, USA
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Prokof'ev N, Svistunov B. Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations. PHYSICAL REVIEW LETTERS 2004; 92:015703. [PMID: 14754002 DOI: 10.1103/physrevlett.92.015703] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2002] [Indexed: 05/24/2023]
Abstract
We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid-Mott-insulator transition.
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Affiliation(s)
- Nikolay Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Alet F, Sørensen ES. Directed geometrical worm algorithm applied to the quantum rotor model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:026702. [PMID: 14525143 DOI: 10.1103/physreve.68.026702] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2003] [Revised: 05/27/2003] [Indexed: 05/24/2023]
Abstract
We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm the Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part, is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore, we show how correlation functions C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and undirected geometrical worm algorithms. Results for autocorrelation times and Green's functions are presented for the quantum rotor model.
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Affiliation(s)
- Fabien Alet
- Computational Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland.
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