Pseudocriticality in antiferromagnetic spin chains

TL;DR

This study investigates pseudocriticality in an SU(N) antiferromagnetic spin chain, revealing proximity to complex conformal field theories and demonstrating pseudocritical behavior through advanced quantum Monte Carlo simulations.

Contribution

It provides the first detailed numerical analysis of a 1+1D SU(N) model near a complex CFT, linking pseudocriticality to complex conformal field theories and extending understanding of deconfined criticality.

Findings

Excellent agreement with CFT predictions for central charge as a function of N

Identification of pseudocritical behavior near complex CFTs for N>2

Connection of the N=3 case to the spin-1 biquadratic model and its pseudocriticality

Abstract

Weak first-order pseudocriticality with approximate scale invariance has been observed in a variety of settings, including the intriguing case of deconfined criticality in 2+1 dimensions. Recently, this has been interpreted as extremely slow flows ("walking behavior") for real-valued couplings in proximity to a bona fide critical point with complex-valued couplings, described by a complex conformal field theory (CFT). Here we study an SU($N$) generalization of the the Heisenberg antiferromagnet, which is a familiar model for deconfined criticality in 2+1 dimensions. We show that in 1+1 dimensions the model is located near a complex CFT, whose proximity can be tuned as a function of $N$. We employ state-of-the-art quantum Monte Carlo simulations for continuous $N$ along with an improved loop estimator for the R\'{e}nyi entanglement entropy based on a nonequilibrium work protocol. These techniques allow us to track the central charge of this model in detail as a function of $N$, where we observe excellent agreement with CFT predictions. Notably, this includes the region $N>2$, where the CFT moves into the complex plane and pseudocritical drifts enable us to recover the real part of the complex central charge with remarkable accuracy. Since the present model with $N=3$ is also equivalent to the spin-1 biquadratic model, our work sheds new light on the dimerized phase of the spin-1 chain, demonstrating that it is pseudocritical and proximate to a complex CFT.