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Bulletin of the American Physical Society

Deconfined quantum criticality in two-dimensional bipartite SU(N) anti-ferromagnets

Ribhu K. Kaul

Published Mar 3, 2014• 0 citations
OpenAlex

Abstract

I will give an overview of unbiased numerical work on the Neelvalence bond solid (VBS) phase transition in d = 2 antiferromagnets. 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 ≤ N ≤ 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 × 256 spins, the crucial role of Berry phases at the critical point has been verified, strong evidence for non-compact CPN−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 CPN−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.

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I will give an overview of unbiased numerical work on the Neelvalence bond solid (VBS) phase transition in d = 2 antiferromagnets. 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 ≤ N ≤ 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 × 256 spins, the crucial role of Berry phases at the critical point has been verified, strong evidence for non-compact CPN−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 CPN−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.
We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order and competing six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector K=(2π/3,-2π/3). We present quantum Monte Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.
We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.
We present a detailed study of the destruction of SU(NNN) magnetic order in square lattice bilayer antiferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(NNN) N\'eel state into two distinct quantum disordered ``valence-bond'' phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry-breaking valence-bond solid (VBS) state. For finite interlayer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the N\'eel-VBS transition is first order for all $N\ensuremath{\ge}5$ accesible in our model, whereas the N\'eel-VBL transition is continuous for N=2N=2N=2 and first order for $N\ensuremath{\ge}4$; for N=3N=3N=3 the N\'eel-VBL transition show no signs of first-order behavior.
We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transition between two such VBS phases is studied. In some cases, an interesting second-order transition controlled by a fixed line with varying critical exponents is found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1∕21∕21∕2 spinon excitations emerge right at the transition. The low-energy physics of this critical point (up to marginally irrelevant interactions) contains just a free quadratically dispersing ``photon.'' The phase structure on one side of this continuous transition is very intricate, consisting of a series of infinitely closely spaced further transitions in a ``devil's staircase'' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a nongeneric multicritical point.
Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.
In this manuscript we review recent developments in the numerical simulations of bipartite SU( N ) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O (10 5 ) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions - a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the "designer" Hamiltonians.