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Physics

Does quantum mechanics play a role in critical phenomena?

Rajiv R. P. Singh

Published Apr 26, 2010• 9 citations
Publisher

Abstract

The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S ¼ 1=2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations.The results support a continuous transition of the ground state, in agreement with the theory of ''deconfined'' quantum criticality.There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated.This suggests that either the SUðNÞ symmetric noncompact CP NÀ1 field theory for deconfined quantum criticality has to be revised or that the theory for N ¼ 2 (as in the system studied here) differs significantly from N ! 1 (where the field theory is analytically tractable).

DOI
10.1103/physics.3.35

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The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S ¼ 1=2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations.The results support a continuous transition of the ground state, in agreement with the theory of ''deconfined'' quantum criticality.There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated.This suggests that either the SUðNÞ symmetric noncompact CP NÀ1 field theory for deconfined quantum criticality has to be revised or that the theory for N ¼ 2 (as in the system studied here) differs significantly from N ! 1 (where the field theory is analytically tractable).
The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.
To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(NNN) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(NNN) N\'eel and valence-bond solid phases is characterized for N=2N=2N=2, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (L=256L=256L=256) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\ensuremath{\equiv}1/\ensuremath{\nu}$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\ensuremath{\Psi}}^{2}$ for the SU(3) model.
We discuss zero‐temperature phase transititions from an antiferromagnetic ground state into a valence‐bond‐solid (VBS) in two different square‐lattice quantum spin models. In one limit these models reduce to the standard S = 1/2 XY and Heisenberg models, respectively, which have long‐range antiferromagnetic order at T = 0. Introducing particular types of four‐spin interactions, amenable to quantum Monte Carlo (QMC) simulation without negative‐sign problems, drives phase transitions into VBS states with broken Z4 symmetry. It has recently been argued that continuous quantum phase transitions of this nature represent a new class of deconfined quantum‐critical points [Senthil et al., Science 303, 1490 (2004)], which are not captured within the standard Ginzburg‐Landau framework of phase transitions. Here we discuss a QMC study aimed at accurately characterizing the transition in the XY model. We find some evidence that the transition is actually weakly first‐order, but other scenarios, such as a continuous transition violating hyperscaling, also cannot be completely ruled out. For the Heisenberg model with four‐spin interactions we have confirmed that a VBS state exists. Preliminary finite‐size scaling results show consistency with a continuous transition into the Néel state, with dynamic exponent z = 1. This model is thus a candidate for deconfined quantum criticality.
We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin QQQ-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at Qc=0.310(11)Q_{c}=0.310(11)Qc​=0.310(11), and obtain the critical exponents at QcQ_{c}Qc​, including ys=0.81(4)y_{s}=0.81(4)ys​=0.81(4) and the scaling dimensions of AF and VBS order parameters Δs=0.660(15)Δ_{s}=0.660(15)Δs​=0.660(15) and Δv=0.204(14)Δ_{v}=0.204(14)Δv​=0.204(14). The weak long-range AF order for $Q