Superconductor-insulator transition in two-dimensional dirty boson systems

Extraordinary-log Universality of Critical Phenomena in Plane Defects

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.

Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets

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.

Superconductor-insulator transition in two-dimensional indium-indium-oxide composite

The magnetic-field-tuned superconductor-to-insulator transition was studied in a hybrid system of superconducting indium islands, deposited on an indium oxide (InOx) thin film, which exhibits global superconductivity at low magnetic fields. Vacuum annealing was used to tune the conductivity of the InOx film, thereby tuning the inergrain coupling and the nature of the transition. The hybrid system exhibits a "giant" magnetoresistance above the magnetic-field-tuned superconductor-to-insulator transition (H-SIT), with critical behavior similar to that of uniform InOx films but at much lower magnetic fields, that manifests the duality between Cooper pairs and vortices. A key feature of this hybrid system is the separation between the quantum criticality and the onset of nonequilibrium behavior.

Collective Modes at a Disordered Quantum Phase Transition

We study the collective excitations, i.e., the Goldstone (phase) mode and the Higgs (amplitude) mode, near the superfluid-Mott glass quantum phase transition in a two-dimensional system of disordered bosons. Using Monte Carlo simulations as well as an inhomogeneous quantum mean-field theory with Gaussian fluctuations, we show that the Higgs mode is strongly localized for all energies, leading to a noncritical scalar response. In contrast, the lowest-energy Goldstone mode undergoes a striking delocalization transition as the system enters the superfluid phase. We discuss the generality of these findings and experimental consequences, and we point out potential relations to many-body localization.

Imaging quantum fluctuations near criticality

A quantum phase transition (QPT) occurs between two competing phases of matter at zero temperature, driven by quantum fluctuations. Though the presence of these fluctuations is well established, they have not been locally imaged in space and their local dynamics has not been studied so far. We use a scanning superconducting quantum interference device to image quantum fluctuations in the vicinity of the QPT from a superconductor to an insulator. We find fluctuations of the diamagnetic response in both space and time that survive well below the transition temperature, demonstrating their quantum nature. The fluctuations appear as telegraph-like noise with a range of characteristic times and a non-monotonic temperature dependence, revealing unexpected quantum granularity. The lateral dimension of these fluctuations grows towards criticality, offering a new measurable length scale. Our results provide physical insight about the reorganization of phases across a QPT, with implications for any theoretical description. This paves a new route for future quantum information applications.

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

Soft Coulomb gap and asymmetric scaling towards metal-insulator quantum criticality in multilayer MoS2

Quantum localization–delocalization of carriers are well described by either carrier–carrier interaction or disorder. When both effects come into play, however, a comprehensive understanding is not well established mainly due to complexity and sparse experimental data. Recently developed two-dimensional layered materials are ideal in describing such mesoscopic critical phenomena as they have both strong interactions and disorder. The transport in the insulating phase is well described by the soft Coulomb gap picture, which demonstrates the contribution of both interactions and disorder. Using this picture, we demonstrate the critical power law behavior of the localization length, supporting quantum criticality. We observe asymmetric critical exponents around the metal-insulator transition through temperature scaling analysis, which originates from poor screening in insulating regime and conversely strong screening in metallic regime due to free carriers. The effect of asymmetric scaling behavior is weakened in monolayer MoS₂ due to a dominating disorder.

The interplay between strong interactions and presence of disorder makes atomically thin transition metal dichalcogenides an ideal platform to study phase transitions and critical phenomena. Here, the authors observe asymmetric critical exponents around the metal-insulator-transition of multilayer MoS₂.

Localization of Interacting Dirac Fermions

Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.

Quantum Correlations, Separability, and Quantum Coherence Length in Equilibrium Many-Body Systems

Nonlocality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Because of nonlocality, mixed states of any two subsystems are correlated in a stronger way than what can be accounted for by considering the correlated probabilities of occupying some microstates. In the case of equilibrium mixed states, we explicitly build two-point quantum correlation functions, which capture the specific, superior correlations of quantum systems at finite temperature, and which are directly accessible to experiments when correlating measurable properties. When nonvanishing, these correlation functions rule out a precise form of separability of the equilibrium state. In particular, we show numerically that quantum correlation functions generically exhibit a finite quantum coherence length, dictating the characteristic distance over which degrees of freedom cannot be considered as separable. This coherence length is completely disconnected from the correlation length of the system-as it remains finite even when the correlation length of the system diverges at finite temperature-and it unveils the unique spatial structure of quantum correlations.

Self-optimized superconductivity attainable by interlayer phase separation at cuprate interfaces

Stabilizing superconductivity at high temperatures and elucidating its mechanism have long been major challenges of materials research in condensed matter physics. Meanwhile, recent progress in nanostructuring offers unprecedented possibilities for designing novel functionalities. Above all, thin films of cuprate and iron-based high-temperature superconductors exhibit remarkably better superconducting characteristics (for example, higher critical temperatures) than in the bulk, but the underlying mechanism is still not understood. Solving microscopic models suitable for cuprates, we demonstrate that, at an interface between a Mott insulator and an overdoped nonsuperconducting metal, the superconducting amplitude is always pinned at the optimum achieved in the bulk, independently of the carrier concentration in the metal. This is in contrast to the dome-like dependence in bulk superconductors but consistent with the astonishing independence of the critical temperature from the carrier density x observed at the interfaces of La2CuO4 and La2-x Sr x CuO4. Furthermore, we identify a self-organization mechanism as responsible for the pinning at the optimum amplitude: An emergent electronic structure induced by interlayer phase separation eludes bulk phase separation and inhomogeneities that would kill superconductivity in the bulk. Thus, interfaces provide an ideal tool to enhance and stabilize superconductivity. This interfacial example opens up further ways of shaping superconductivity by suppressing competing instabilities, with direct perspectives for designing devices.

Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to the Einstein-Maxwell theory in an asymptotically four-dimensional anti-de Sitter space spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond nonperturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

Anomalous quantum glass of bosons in a random potential in two dimensions

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.

Order-by-disorder and quantum Coulomb phase in quantum square ice

We show that quantum square ice-namely, the two-dimensional version of proton or spin ice with tunable quantum tunneling of the electric or magnetic dipole moment-exhibits a quantum spin-liquid phase supporting fractionalized spinons. This phase corresponds to a thermally induced, deconfined quantum Coulomb phase of a two-dimensional lattice gauge theory. It emerges at finite, yet exceedingly low temperatures from the melting of two distinct order-by-disorder phases appearing in the ground state: a plaquette valence-bond solid for low tunneling; and a canted Néel state for stronger tunneling. The latter phases appear via the highly nonlinear effect of quantum fluctuations within the degenerate manifold of ice-rule states, and they can be identified as the two competing ground states of a discrete lattice gauge theory (quantum link model) emerging as the effective Hamiltonian of the system within degenerate perturbation theory.

Critical exponents of the superfluid-Bose-glass transition in three dimensions

Recent experimental and numerical studies of the critical-temperature exponent ϕ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, ϕ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal-fluid transition-temperature dependence on the chemical potential (or the magnetic field, in spin systems), T_{c}∝(μ-μ_{c})^{ϕ}, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the ϕ=νz law [with ϕ=2.7(2), z=3, and ν=0.88(5)] holds true, resolving the ϕ-exponent "crisis."

Thermometry of cold atoms in optical lattices via artificial gauge fields

Artificial gauge fields are a unique way of manipulating the motional state of cold atoms. Here we propose the use (practical or conceptual) of artificial gauge fields--obtained, e.g., experimentally via lattice shaking or conceptually via a Galilean transformation--to perform primary noise thermometry of cold atoms in optical lattices, not requiring any form of prior calibration. The proposed thermometric scheme relies on fundamental fluctuation--dissipation relations, connecting the global response to the variation of the applied gauge field and the fluctuation of quantities related to the momentum distribution (such as the average kinetic energy or the average current). We demonstrate gauge-field thermometry for several physical situations, including free fermions and interacting bosons. The proposed approach is extremely robust to quantum fluctuations-even in the vicinity of a quantum phase transition--when it relies on the thermal fluctuations of an emerging classical field, associated with the onset of Bose condensation or chiral order.

Bose-glass transition and spin-wave localization for 2D bosons in a random potential

A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential μ=±W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Ω(c) decreasing with W, and presumably vanishing in the Bose-glass phase.

Disordered bosons in one dimension: from weak- to strong-randomness criticality

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.

Quantum critical dynamics simulation of dirty boson systems

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.

Absence of a direct superfluid to mott insulator transition in disordered bose systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid-insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound Delta(c) corresponding to the onset of disorder-induced superfluidity, satisfies the relation Delta(c)>Eg/2, with Eg/2 the half-width of the Mott gap in the pure system.

Instanton glass generated by noise in a Josephson-junction array

We compute the correlation function of a superconducting order parameter in a continuous model of a two-dimensional Josephson-junction array in the presence of a weak Gaussian noise. When the Josephson coupling is large compared to the charging energy, the correlations in the Euclidian space decay exponentially at low temperatures regardless of the strength of the noise. We interpret such a state as a collective Cooper-pair insulator and argue that it resembles properties of disordered superconducting films.

SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.

Giant proximity effect in a phase-fluctuating superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.

Collective Cooper-pair transport in the insulating state of Josephson-junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are nonmonotonic functions of the magnetic field. We propose that formation of the dynamic Coulomb barrier and its size scaling are consequences of the mutual Josephson phase synchronization across the system. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.

Finite-temperature phase transitions in a two-dimensional boson Hubbard model

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.

Quantum phase transitions of hard-core bosons in background potentials

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.

Universal scaling of the conductivity at the superfluid-insulator phase transition

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.

Drag effect and topological complexes in strongly interacting two-component lattice superfluids

The mutual drag in strongly interacting two-component superfluids in optical lattices is discussed. Two competing drag mechanisms are the vacancy-assisted motion and proximity to a quasimolecular state. In a case of strong drag, the lowest energy topological excitation (vortex or persistent current) can consist of several circulation quanta. In the SQUID-type geometry, the circulation can become fractional. We present both the mean field and Monte Carlo results. The drag effects in optical lattices are drastically different from the Galilean-invariant Andreev-Bashkin effect in liquid helium.

Superfluid-insulator transition in a commensurate one-dimensional bosonic system with off-diagonal disorder

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.

Superfluid interfaces in quantum solids

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.

Generalized anisotropic scaling theory and the transverse meissner transition

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.

Weak first-order superfluid-solid quantum phase transitions

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.

Commensurate two-component bosons in an optical lattice: ground state phase diagram

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.

Superfluid-superfluid phase transitions in a two-component Bose-Einstein condensate

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.

Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations

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.

Directed geometrical worm algorithm applied to the quantum rotor model

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.

Cluster Monte Carlo algorithm for the quantum rotor model

We propose a highly efficient "worm"-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with mu=0, the algorithm yields high- precision estimates for the critical point K(c)=0.333 05(5) and the correlation length exponent nu=0.670(3). For the disordered case, mu=1 / 2+/-1 / 2, we find nu=1.15(10).

Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet

The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.

Vortex glass transition in a random pinning model

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.

Phase diagram of a disordered boson Hubbard model in two dimensions

We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent z = 1.35+/-0.05 and the correlation length critical exponent nu = 0.67+/-0.03. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z = 1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z = 1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that balance between the two may lead to charged quantum critical points at which z = 1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D = 3 - epsilon. Precisely in D = 3, however, the above simple result breaks down, and z > 1. Relation to other studies is discussed.