Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A23: Invited Session: Phase Transitions in Classical and Quantum Lattice Models |
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Sponsoring Units: DCOMP GSNP Chair: Anders Sandvik, Boston University Room: 505-507 |
Monday, March 3, 2014 8:00AM - 8:36AM |
A23.00001: Aneesur Rahman Prize: The Inverse Ising Problem Invited Speaker: Robert Swendsen Many methods are available for carrying out computer simulations of a model Hamiltonian to obtain thermodynamic information by generating a set of configurations. The inverse problem consists of recreating the parameters of the Hamiltonian, given a set of configurations. The problem arises in a variety of contexts, and there has been much interest recently in the inverse Ising problem, in which the configurations consist of Ising spins. I will discuss an efficient method for solving the problem and what it can tell us about the Sherrington-Kirkpatrick model. [Preview Abstract] |
Monday, March 3, 2014 8:36AM - 9:12AM |
A23.00002: Deconfined quantum criticality in two-dimensional bipartite SU(N) anti-ferromagnets Invited Speaker: Ribhu Kaul I will give an overview of unbiased numerical work on the N\'eel- valence bond solid (VBS) phase transition in $d=2$ anti-ferromagnets. This progress has been possible due to the discovery of a new class of Hamiltonians of SU($N$) spins that are free of the sign problem of quantum Monte Carlo. I will show through extensive numerical studies of the quantum phase transition on a variety of bipartite systems: square, rectangular, honeycomb and square bilayer, for a number of values of $N$ ($2 \leq N \leq 10$), that a close to complete picture of an unusual ``deconfined critical point'' has emerged. Significantly, no direct evidence for first order behavior has been found on the largest simulations with $256\times 256$ spins, the crucial role of Berry phases at the critical point has been verified, strong evidence for non-compact CP$^{N-1}$ universality is evident for a range of $N$ values, the inferred ``dangerous'' (ir)relevance of lattice anisotropy at the critical point is consistent with various limiting analytic calculations on the CP$^{N-1}$ field theory and close to the critical point dramatic signatures of the emergent photon excitation have been detected in VBS correlation functions. I will conclude with some open theoretical issues that remain to be resolved and possible experimental realizations. [Preview Abstract] |
Monday, March 3, 2014 9:12AM - 9:48AM |
A23.00003: Deconfined Quantum Criticality and Phase Transitions in 3D Classical Loop Models Invited Speaker: John Chalker I will talk about the statistical physics of a family of three-dimensional lattice models for completely-packed loops that have transitions between phases of two types: one in which there are only short loops, and another in which some loops are extended. The models can be viewed as lattice discretisations of $CP^{n-1}$ sigma models in 3D. Alternatively, they can be seen as quantum $SU(n)$ quantum magnets in (2+1)D. In this case, the phase with long loops is a Neel phase, the phase with only short loops is a valence bond phase, and the models are closely related to loop algorithms developed for quantum Monte Carlo simulations. Depending on the design of the model, the short loop phase is either unique (representing a valence bond liquid) or spontaneously breaks a spatial symmetry (representing a valence bond solid). The transition from the Neel phase to the valence bond solid is a candidate deconfined critical point and the loop model gives access to this transition via Monte Carlo simulations. I will present results from large-scale simulations of the transition. \\[4pt] [1] Adam Nahum, J. T. Chalker, P. Serna, M. Ortuno, and A. M. Somoza, Phys. Rev. Lett. {\bf 107} 110601 (2011).\\[0pt] [2] Adam Nahum, J. T. Chalker, P. Serna, M. Ortuno, and A. M. Somoza, Phys. Rev. B {\bf 88}, 134411 (2013).\\[0pt] [3] Adam Nahum, J. T. Chalker, P. Serna, M. Ortuno, and A. M. Somoza, in preparation. [Preview Abstract] |
Monday, March 3, 2014 9:48AM - 10:24AM |
A23.00004: Quantum phase diagrams and phase transitions in frustrated two-dimensional Heisenberg models Invited Speaker: Donna Sheng The quantum spin liquid is an emergent state of matter, which has attracted a lot of recent attention. I will review recent numerical progress based on the density matrix renormalization calculations in identifying gapped spin liquid in two-dimensional frustrated spin systems. I will first focus on extended model with Heisenberg exchange couplings on kagome lattice and demonstrate a topological state with fractionalized spinon and emergent gauge field clearly shown in numerical simulations. I will present concrete results on the quantum phase diagram of the extended kagome Heisenberg model, and compare that with the phase diagrams of the square and honeycomb lattice models with the dominant plaquette valence bond phase in nonmagnetic region. I will discuss numerical effort and theoretical challenge in fully pinning down the nature of the gapped topological phase, and also the nature of the quantum phase transitions in these Heisenberg systems. [Preview Abstract] |
Monday, March 3, 2014 10:24AM - 11:00AM |
A23.00005: Mott Transitions of Correlated Dirac Fermions from SU(2) to SU($N$) Invited Speaker: Thomas C. Lang The rise of graphene and topological insulators has sparked countless investigations of interacting electrons on the honeycomb lattice. We present recent advances in the study of the evolution from the weak-coupling semimetal into the strong-coupling, insulating regime by means of unbiased quantum Monte Carlo simulations of the Hubbard and related models on the honeycomb lattice at half filling. Employing a novel approach to quantum phase transitions, we perform non-equilibrium imaginary time quenches of the Hubbard model in (zero temperature) projective quantum Monte Carlo simulations. This allows us to efficiently access order parameters on a finite size lattice for a wide range of coupling values in a single run. We extract reliable estimates for the scaling properties and critical exponents of the semimetal-insulator quantum phase transition. Furthermore, we investigate the extension of the Hubbard model with an explicit SU($N$)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction. From the large-$N$ regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-$N$ limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. Furthermore, we discuss the new possibility to efficiently access the Renyi entanglement entropy within the auxiliary field quantum Monte Carlo algorithm. Using the example of a correlated topological insulator we present the development of the stable computation of higher order Renyi entropies, in order to access the entanglement spectrum. [Preview Abstract] |
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