arXiv subjects

Anders W. Sandvik

Publications and source records attributed to Anders W. Sandvik.

At least 73 records · Page 4Linked to original sources

arXiv2018

Dynamic scaling of topological ordering in classical systems

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional $\mathbb{Z}_2$ (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a non-local order parameter (defined using Wilson loops) and a dynamic exponent $z=2.70 \pm 0.03$, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature---the Ising chain, the two-dimensional $\mathbb{Z}_2$ gauge model, and a three-dimensional star model (another variant of the $\mathbb{Z}_2$ gauge model). In these systems the correlation length diverges exponentially, in a way that is non-smooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.

cond-mat.stat-mech↗

arXiv2017

Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet

We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($δ$-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)$_2$$\cdot$4D$_2$O, where a broad spectral-weight continuum at $q=(π,0)$ was interpreted as deconfined spinons. Our results at $(π,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(π/2,π/2)$ (as also seen experimentally). Turning on $Q$, we observe a rapid reduction of the $(π,0)$ magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret the picture of deconfined spinons at $(π,0)$ in the experiments as nearly deconfined spinons---a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(π,0)$-magnon in the Heisenberg model and its depletion in the $J$-$Q$ model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the $(π,0)$ and $(π/2,π/2)$ features of the Heisenberg model. It can also account for the rapid loss of the $(π,0)$ magnon with increasing $Q$ and a remarkable persistence of a large magnon pole at $q=(π/2,π/2)$ even at the deconfined critical point.

cond-mat.str-el↗

arXiv2017

Dynamic scaling in the 2D Ising spin glass with Gaussian couplings

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $τ$ to the system length $L$; $τ\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.

cond-mat.stat-mech↗

arXiv2017

Modulated phases in a three-dimensional Maier-Saupe model with competing interactions

This work is dedicated to the study of the discrete version of the Maier-Saupe model in the presence of competing interactions. The competition between interactions favoring different orientational ordering produces a rich phase diagram including modulated phases. Using a mean-field approach and Monte Carlo simulations, we show that the proposed model exhibits isotropic and nematic phases and also a series of modulated phases that meet at a multicritical point, a Lifshitz point. Though the Monte Carlo and mean-field phase diagrams show some quantitative disagreements, the Monte Carlo simulations corroborate the general behavior found within the mean-field approximation.

cond-mat.stat-mech↗

arXiv2017

Duality between the deconfined quantum-critical point and the bosonic topological transition

Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.

cond-mat.str-el↗

arXiv2017

Field-driven quantum phase transitions in $S=1/2$ spin chains

We study the magnetization process of a 1D extended Heisenberg model, the $J$-$Q$ model, as a function of an external magnetic field. In this model, $J$ represents the traditional antiferromagnetic Heisenberg exchange and $Q$ is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value $q_c\approx 0.85$ where $q\equiv Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for $q>q_{\rm min}$, where we have calculated $q_{\rm min}=2/9$ exactly. For $q>q_{\rm min}$ two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for $q>q_{\rm min}$. Our results show that neither geometric frustration nor spin-anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated $J_1$-$J_2$ chain ($J_1>0$, $J_2<0$), but only if $J_2$ is spin-anisotropic. We also investigate quantum-critical scaling near the transition into the fully polarized state for $q\le q_{\rm min}$ at $T>0$. While the expected `zero-scale-factor' universality is clearly seen for $q=0$ and $q\ll q_{\rm min}$; closer to $q_{\rm min}$ we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at $q_{\rm min}$, which leads to a cross-over at a temperature $T^*(q)$ between logarithmic tricritical scaling and zero-scale-factor universality, with $T^*(q)\to 0$ when $q\to q_{\rm min}$.

cond-mat.str-el↗

arXiv2017

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature $T=0$ of the two-dimensional Ising model with random $J= \pm 1$ couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, $τ\sim L^z$, are $z=8.28 \pm 0.03$ for the relaxation of the order parameter and $z=10.31 \pm 0.04$ for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for $T \to 0$ simulated annealing are different from the temperature-dependent equilibrium dynamic exponent $z_{\rm eq}(T)$, for which previous studies have found a divergent behavior; $z_{\rm eq}(T\to 0) \to \infty$. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.

cond-mat.stat-mech↗

arXiv2017

Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators

The entanglement entropy (EE) of quantum systems is often used as a test of low-energy descriptions by conformal field theory (CFT). Here we point out that this is not a reliable indicator, as the EE often shows the same behavior even when a CFT description is not correct (as long as the system is asymptotically scale-invariant). We use constraints on the scaling dimension given by the CFT with SU(2) symmetry to provide alternative tests with two- and four-point correlation functions, showing examples for quantum spin models in 1+1 dimensions. In the case of a critical amplitude-product state expressed in the valence-bond basis (where the amplitudes decay as a power law of the bond length and the wave function is the product of all bond amplitudes), we show that even though the EE exhibits the expected CFT behavior, there is no CFT description of this state. We provide numerical tests of the behavior predicted by CFT for the correlation functions in the critical transverse-field Ising chain and the $J$-$Q$ spin chain, where the conformal structure is well understood. That behavior is not reproduced in the amplitude-product state.

cond-mat.str-el↗

arXiv2016

Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets

In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.

hep-th↗

arXiv2016

Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid

We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S=1/2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multi-spin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (singlet pair) basis from a contribution that can not be generated by the SDRG scheme. In the model with multi-spin couplings, where the clean system dimerizes spontaneously, random singlets form between spinons localized at domain walls in the presence of disorder. This amorphous valence-bond solid is asymptotically a random-singlet state and only differs from the random-exchange Heisenberg chain in its short-distance properties.

cond-mat.str-el↗

arXiv2016

Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point

We study the level structure of excitations at the "deconfined" critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J$-$Q$ model as an example. Energy gaps in different spin ($S$) and momentum (${\bf k}$) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at ${\bf k}=(0,0)$, $(π,0)$, $(0,π)$, and $(π,π)$, as inferred from two-spinon excitations ($S=0$ and $S=1$ states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).

cond-mat.str-el↗

arXiv2016

Quantum criticality with two length scales

The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires discontinuities. Numerous computer simulations have offered no proof of such transitions, however, instead finding deviations from expected scaling relations that were neither predicted by the DQC theory nor conform to standard scenarios. Here we show that this enigma can be resolved by introducing a critical scaling form with two divergent length scales. Simulations of a quantum magnet with antiferromagnetic and dimerized ground states confirm the form, proving a continuous transition with deconfined excitations and also explaining anomalous scaling at T > 0. Our findings revise prevailing paradigms for quantum criticality, with potentially far-reaching implications for many strongly-correlated materials.

cond-mat.str-el↗

arXiv2016

Quantum Monte Carlo studies of spinons in one-dimensional spin systems

Observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many-body physics. Here we further explore a computational scheme [Y. Tang and A. W. Sandvik, Phys. Rev. Lett. {\bf 107}, 157201 (2011)] based on valence-bond quantum Monte Carlo simulations of quantum spin systems. Using several different one-dimensional models, we characterize $S=1/2$ spinon excitations using the spinon size and confinement length (the size of a bound state). The spinons have finite size in valence-bond-solid states, infinite size in the critical region, and become ill-defined in the Néel state. We also verify that pairs of spinons are deconfined in these uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths (dimerization) or coupling two chains (forming a ladder). In the dimerized system an individual spinon can be small when the confinement length is large---this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence-bond-solid (where the spinons are deconfined). Based on our numerical results, we argue that the situation $λ\ll Λ$ is associated with weak repulsive short-range spinon-spinon interactions. In principle both the length-scales can be individually tuned from small to infinite (with $λ\le Λ$) by varying model parameters. In the ladder system the two lengths are always similar, and this is the case also in the dimerized systems when the corresponding uniform chain is in the critical phase. In these systems the effective spinon-spinon interactions are purely attractive and there is only a single large length scale close to criticality, which is reflected in the standard spin correlations as well as in the spinon characteristics.

cond-mat.str-el↗

arXiv2015

Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets

We investigate the quantum phase transition in an $S = 1/2$ dimerized Heisenberg antiferromagnet in three spatial dimensions. By performing large-scale quantum Monte Carlo simulations and detailed finite-size scaling analyses, we obtain high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the antiferromagnetically ordered Néel phase. This transition breaks O($N$) symmetry with $N = 3$ in $D = 3 + 1$ dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization, $m_s$, and the Néel temperature, $T_N$. We present a scaling Ansatz for $T_N$, including logarithmic corrections, which agrees with our data and indicates exact linearity with $m_s$, implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted $N$-independent leading and subleading logarithmic corrections in the size-dependence of the staggered magnetic susceptibility. These logarithmic scaling forms have not previously been identified or verified by unbiased numerical methods and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as TlCuCl$_3$.

cond-mat.str-el↗

arXiv2015

Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet

We use quantum Monte Carlo simulations to study a dimer-diluted $S=1/2$ Heisenberg model on a bilayer square lattice with intralayer interaction $J_{1}$ and interlayer interaction $J_{2}$. Below the classical percolation threshold $p_c$, the system has three phases reachable by tuning the interaction ratio $g=J_{2}/J_{1}$: a N$\acute{e}$el ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution $p$ and interaction ratio $g$. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature $T$ and following a stretched exponential form at $T>0$; $χ_u \sim \exp(-b/T^α)$ with $α< 1$. At the phase transition point from N$\acute{e}$el ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard $O(3)$ universality class in 2+1 dimensions.

cond-mat.str-el↗

arXiv2015

1D valence bond solids in a magnetic field

A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model---the J-Q$_2$ model---using stochastic series expansion quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.

cond-mat.str-el↗

arXiv2015

Velocity of excitations in ordered, disordered and critical antiferromagnets

We test three different approaches, based on quantum Monte Carlo simulations, for computing the velocity $c$ of triplet excitations in antiferromagnets. We consider the standard $S=1/2$ one- and two-dimensional Heisenberg models, as well as a bilayer Heisenberg model at its critical point. Computing correlation functions in imaginary time and using their long-time behavior, we extract the lowest excitation energy versus momentum using improved fitting procedures and a generalized moment method. The velocity is then obtained from the dispersion relation. We also exploit winding numbers to define a cubic space-time geometry, where the velocity is obtained as the ratio of the spatial and temporal lengths of the system when all winding number fluctuations are equal. The two methods give consistent results for both ordered and critical systems, but the winding-number estimator is more precise. For the Heisenberg chain, we accurately reproduce the exactly known velocity. For the two-dimensional Heisenberg model, our results are consistent with other recent calculations, but with an improved statistical precision; $c=1.65847(4)$. We also use the hydrodynamic relation $c^2=ρ_s/χ_\perp(q\to 0)$ between $c$, the spin stiffness $ρ_s$, and the transversal susceptibility $χ_\perp$, using the smallest non-zero momentum $q=2π/L$. This method also is well controlled in two dimensions, but the cubic criterion for winding numbers delivers better numerical precision. In one dimension the hydrodynamic relation is affected by logarithmic corrections which make accurate extrapolations difficult. As an application of the winding-number method, for the quantum-critical bilayer model our high-precision determination of the velocity enables us to quantitatively test, at an unprecedented level, field-theoretic predictions for low-temperature scaling forms where $c$ enters.

cond-mat.str-el↗

arXiv2015

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 2D 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 $κ\sim {\rm exp}(-b/T^α)+c$ 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 four orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp cross-over.

cond-mat.quant-gas↗