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arXiv:2402.04641

Low-lying excited states quantum entanglement and continuous quantum phase transitions: The criticality of a one-dimensional deconfined critical point

Yanchao Li, Yuan-Hang Zhou, Yuan Zhang, Hai‐Qing Lin

Published Feb 7, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2402.04641

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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.
From the perspective of entanglement in low-lying excited states, a profound analysis was carried out regarding the quantum phase transitions within three models that fall outside the Landau-Ginzburg-Wilson (LGW) paradigm. In the context of the deconfined quantum critical point (DQCP) in a one-dimensional quantum spin chain, our findings demonstrate a tight correlation between the reconstruction of low-lying excitation spectra and the DQCP. The precise location of the critical point and its continuous nature can be signaled by the singular behaviors of the entanglement of the first-excited state. Moreover, in comparison with two types of Berezinskii-Kosterlitz-Thouless (BKT) phase transitions, the entanglement presents three different singularity characteristics. These characteristics not only unveil the essence of diverse symmetry types on either side of the DQCP but also expose the disparate causes underlying the formation of the two BKT type phase transitions.
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.
Over past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across physics communities, as it offers a new paradigm beyond the Landau-Ginzburg-Wilson framework. However, the nature of DQCP has been controversial based on conflicting numeric results. In our work, we demonstrate that an anomalous logarithmic behavior in the entanglement entropy (EE) persists in a class of models analogous to the DQCP. On the basis of quantum Monte Carlo computation of the EE on SU( N ) DQCP spin models, we show that for a series of N smaller than a critical value, the anomalous logarithmic behavior always exists, which implies that previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when N ≥ N c with an N c we evaluate to lie between 7 and 8, DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory.
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.
The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of symmetries and their spontaneous breaking -- has been proposed and actively pursued for more than two decades. Various 2D quantum many-body lattice models, both in spin/boson and fermion representations have been tested with the state-of-the-art numerical techniques and field-theoretical analyses, and yet, the conclusion is still controversial. Experimental realizations of DQCP in the quantum magnet SrCu2_22​(BO3_33​)2_22​ and superconducting quantum criticality in 2D material have either shown first order transition or intermediate phase. The tension between the lattice scale details and the requirement from continuum limit, manifested in the form of the inconsistent critical scaling behavior and violations of generic conformal bootstrap bound, has not been resolved. Here we solve these decades-long controversies from the new and fundamental perspective of the quantum entanglement. We develop the incremental algorithm to compute the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data and reveal the universal coefficient of the logarithmic correction therein is negative and at odds with positivity requirement of the conformal field theory. Together with results in other 2D DQCP lattice models (both in fermion and spin systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to valence bond solid DQCPs are not conformal fixed point and naturally explain the experimental difficulties in finding them. This marks the end of the beginning of unambiguous finding of the quantum phase transitions truely beyond the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.
The deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken-symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly-first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study the deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density-matrix renormalization-group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the idea that the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size-scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at the deconfined quantum critical point from the concept of quantum information.