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arXiv:1811.08823 · Physical Review Letters

Role of Noether’s Theorem at the Deconfined Quantum Critical Point

Nvsen Ma, Yi‐Zhuang You, Zi Yang Meng

Published May 3, 2019• 61 citations
arXivHTMLPDF

Abstract

Noether's theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether's theorem at the deconfined quantum critical point (DQCP), which is a quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitation, which could potentially guide the ongoing experimental search for the DQCP in quantum magnets.

DOI
10.1103/physrevlett.122.175701

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Noether's theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether's theorem at the deconfined quantum critical point (DQCP), which is a quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitation, which could potentially guide the ongoing experimental search for the DQCP in quantum magnets.
We perform a numerical study of a spin-1/2 model with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power-law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by the Landau-Ginzburg-Wilson symmetry-breaking theory.
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.
From the perspective of low-lying excited states, we study the deconfined quantum critical point (DQCP) in a one-dimensional quantum spin chain by means of the entanglement entropy and fidelity. Our results show that there is a close connection between the reconstruction of low-lying excitation spectra and the DQCP. The precise position of the critical point and its continuous nature is indicated by the singular behavior of the entanglement and fidelity of the first-excited state. Furthermore, compared with the Berezinskii-Kosterlitz-Thouless type phase transitions, which also go beyond the scope of Landau-Ginzburg-Wilson paradigm, we attempt to reveal the essence of different types of symmetries on both sides of the DQPT from different manifestations of entanglement singularity.
Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled n=2n=2n=2 Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous U(1)U(1)U(1) symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.
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.
As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q3_33​ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems.