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Rajak A, Suzuki S, Dutta A, Chakrabarti BK. Quantum annealing: an overview. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210417. [PMID: 36463923 DOI: 10.1098/rsta.2021.0417] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 08/22/2022] [Indexed: 06/17/2023]
Abstract
In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: we especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Atanu Rajak
- Department of Physics, Presidency University, Kolkata 700073, India
| | - Sei Suzuki
- Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
| | - Amit Dutta
- Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Bikas K Chakrabarti
- Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
- Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Kovács IA, Iglói F. Geometry of rare regions behind Griffiths singularities in random quantum magnets. Sci Rep 2022; 12:1074. [PMID: 35058527 PMCID: PMC8776845 DOI: 10.1038/s41598-022-05096-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 12/24/2021] [Indexed: 12/04/2022] Open
Abstract
In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two- and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the energy clusters are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional.
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Affiliation(s)
- István A Kovács
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, 60208, USA.
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, Budapest, 1525, Hungary
- Institute of Theoretical Physics, Szeged University, Szeged, 6720, Hungary
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Zhao J, Wang YC, Yan Z, Cheng M, Meng ZY. Scaling of Entanglement Entropy at Deconfined Quantum Criticality. PHYSICAL REVIEW LETTERS 2022; 128:010601. [PMID: 35061478 DOI: 10.1103/physrevlett.128.010601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 11/24/2021] [Indexed: 05/10/2023]
Abstract
We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that, at a conformally invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections, and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where we still observe similar scaling behavior, but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with the positivity condition of the Rényi entanglement entropy, which holds for unitary conformal field theories (CFTs). Our results unambiguously reveal fundamental differences between DQC and quantum critical points described by unitary CFTs.
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Affiliation(s)
- Jiarui Zhao
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Yan-Cheng Wang
- School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China
| | - Zheng Yan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China
| | - Meng Cheng
- Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
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Agrawal U, Gopalakrishnan S, Vasseur R. Quantum Criticality in the 2D Quasiperiodic Potts Model. PHYSICAL REVIEW LETTERS 2020; 125:265702. [PMID: 33449710 DOI: 10.1103/physrevlett.125.265702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic q-state Potts model in 2+1D. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of q, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be ν=1, saturating a modified version of the Harris-Luck criterion.
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Affiliation(s)
- Utkarsh Agrawal
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Kovács IA, Iglói F. Renormalization group study of random quantum magnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:404204. [PMID: 21931186 DOI: 10.1088/0953-8984/23/40/404204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erdős-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.
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Affiliation(s)
- István A Kovács
- Department of Physics, Loránd Eötvös University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary.
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Jacobsen JL, Saleur H. Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model. PHYSICAL REVIEW LETTERS 2008; 100:087205. [PMID: 18352661 DOI: 10.1103/physrevlett.100.087205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2007] [Revised: 01/08/2008] [Indexed: 05/26/2023]
Abstract
We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.
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Affiliation(s)
- J L Jacobsen
- LPTMS, Université Paris-Sud, Bâtiment 100, 91405 Orsay, France
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Hoyos JA, Kotabage C, Vojta T. Effects of dissipation on a quantum critical point with disorder. PHYSICAL REVIEW LETTERS 2007; 99:230601. [PMID: 18233349 DOI: 10.1103/physrevlett.99.230601] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2007] [Indexed: 05/25/2023]
Abstract
We study the effects of dissipation on a disordered quantum phase transition with O(N) order-parameter symmetry by applying a strong-disorder renormalization group to the Landau-Ginzburg-Wilson field theory of the problem. We find that Ohmic dissipation results in a nonperturbative infinite-randomness critical point with unconventional activated dynamical scaling while super-Ohmic damping leads to conventional behavior. We discuss applications to the superconductor-metal transition in nanowires and to the Hertz theory of the itinerant antiferromagnetic transition.
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Affiliation(s)
- José A Hoyos
- Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65409, USA
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