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arXiv:cond-mat/0501052

Ginzburg-Landau-Wilson Aspect of Deconfined Criticality

Anatoly B. Kuklov, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Jan 4, 2005• 1 citation
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Abstract

Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg-Landau theory. Wilson renormalization argument in combination with the absence of the data collapse even in the regime of weak interaction between the spinons casts a serious doubt on the possibility of the continuous deconfinement transition. We also argue that if a continuous deconfined criticality does exist on the phase diagram, its nature is analogous, in a certain precise sense, to that of the XY universality class.

DOI
10.48550/arxiv.cond-mat/0501052

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Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg-Landau theory. Wilson renormalization argument in combination with the absence of the data collapse even in the regime of weak interaction between the spinons casts a serious doubt on the possibility of the continuous deconfinement transition. We also argue that if a continuous deconfined criticality does exist on the phase diagram, its nature is analogous, in a certain precise sense, to that of the XY universality class.
Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg- Landau theory. Wilson renormalization argument in combination with the absence of the data collapse even in the regime of weak interaction between the spinons casts a serious doubt on the possibility of the continuous deconfinement transition. We also argue that if a continuous deconfined criticality does exist on the phase diagram, its nature is analogous, in a certain precise sense, to that of the XY universality class
We examine recent theoretical predictions for two-dimensional lattice bosonic/spin systems that superfluid-solid (SF-S) quantum phase transitions are often continuous and do not fit the canonical Ginzburg-Landau-Wilson (GLW) picture.We show that the GLW theory based on extended broken symmetry is consistent with existing numerical data, which report weak first-order transitions or problems with the finite-size scaling.This GLW theory excludes generic continuous SF-S transitions and quantum disordered phases.Remarkably, the phase diagram of the deconfined critical action itself features a weak first-order phase transition with spinon deconfinement, in accordance with the conventional theory.Problems with data collapse even in the regime of weak interactions between the spinons strongly suggest that the first-order deconfinement transition is the only possible outcome. * )Since the first study of the SF-VBS point within the J-current model, we have observed numerous first-order SF-VBS transitions for different sets of Hamiltonian parameters.
There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear-deconfine-at the critical point. Nevertheless, many numerical Monte Carlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane CP^{1} antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub frozen. At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.
Unraveling Deconfined Quantum Criticality in Non-Hermitian Easy-Plane JJJ-QQQ Model
Deconfined quantum critical point (DQCP) characterizes the continuous transition beyond Landau-Ginzburg-Wilson paradigm, occurring between two phases that exhibit distinct symmetry breaking. The debate over whether genuine DQCP exists in physical SU(2) spin systems or the transition is weakly first-order has persisted for many years. In this letter, we construct a non-Hermitian easy-plane JJJ-QQQ model and perform sign-problem-free quantum Monte Carlo (QMC) simulation to explore the impact of non-Hermitian microscopic interactions on the transition that potentially features a DQCP. Our results demonstrate that the intensity of the first-order transitions significantly diminishes with the amplification of non-Hermitian interactions, serving as numerical evidence to support the notion that the transition in JJJ-QQQ model is quasi-critical, possibly in the vicinity of the fixed point governing DQCP in the complex plane, described by a non-unitary conformal field theory (CFT). The non-Hermitian interaction facilitates the approach towards such a complex fixed point in the parameter regime. Furthermore, our QMC study on the non-Hermitian J-Q model opens a new route to numerically investigating the nature of complex CFT in the microscopic model.
Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm.A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions.In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1=2 quantum antiferromagnet in the deep easy-plane limit.A check of this conjecture is important for understanding the phase structure of Mott insulators.To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the S 1=2 sector.The result is a first-order phase transition, thus contradicting the conjecture.