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arXiv:2204.01740 · Physical review. B./Physical review. B

Height-conserving quantum dimer models

Zheng Yan, Zi Yang Meng, David A. Huse, Amos Chan

Published Jul 26, 2022• 19 citations
arXivHTMLPDF

Abstract

Quantum dimer models (QDM) are paradigmatic models of strongly correlated systems subject to strong local constraints. Bipartite QDMs admit a dual model of surfaces called height field models. By imposing the lattice sum of height fields as a conserved quantity, the authors show that the Hilbert space ``fragments'', i.e. it splits into disconnected subspaces. Using an emergent spin description and Monte Carlo simulations, the authors obtain the distribution of dynamical exponents within different sectors as well as the ground-state phase diagram.

DOI
10.1103/physrevb.106.l041115

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Quantum dimer models (QDM) are paradigmatic models of strongly correlated systems subject to strong local constraints. Bipartite QDMs admit a dual model of surfaces called height field models. By imposing the lattice sum of height fields as a conserved quantity, the authors show that the Hilbert space ``fragments'', i.e. it splits into disconnected subspaces. Using an emergent spin description and Monte Carlo simulations, the authors obtain the distribution of dynamical exponents within different sectors as well as the ground-state phase diagram.
Strongly constrained quantum systems, in which local rules forbid most configurations, play a central role in condensed matter and lattice gauge theory. Their thermalization is often thought to be delicate: extensive conservation laws and dynamically frozen states can shatter the Hilbert space into many disconnected sectors. A natural question is whether, once the frozen states are removed, the dynamics within a single sector still thermalizes. We address this in the height-conserving quantum dimer model on the square lattice, whose local plaquette flips conserve an emergent height field. Resolving the winding numbers, the four sublattice heights, and lattice momentum , we isolate the dominant connected Krylov component of each fragmented sector and analyze its spectral spectral statistics, entanglement, and connectivity. The two standard chaos diagnostics then show different behavior:across momentum sectors the level-spacing statistics range from near-Poisoon to Wigner-Dyson, yet in every sector the eigenstate entanglement entropy collapses onto a narrow, dome-shaped curve characteristic of eigenstate thermalization. Only a handful of low-entanglement outliers interrupt this thermal pattern, in selected sectors. Thus, strong kinematic constraints can lead to a situation where spectral correlations and eigenstate thermalization need not follow the same universal signatures -- a manifestation of constrained quantum chaos.
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented S=1S=1S=1 dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.
Interacting quantum systems may exhibit fragmentation of their Hilbert space into dynamically disconnected sectors leading to unusual properties like nonergodicity. Fragmentation usually stems from the simultaneous conservation of charge and dipole moment. The authors demonstrate that an alternative scenario occurs in the absence of dipole conservation via a minimal model of interacting spins where fragmentation, including a novel secondary fragmentation in an entangled basis, emerges. A Floquet version of the model yields detectable stroboscopic freezing of certain states at specific drive frequencies.
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented S=1S=1S=1 dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.
While quantum statistical mechanics triumphs in explaining many equilibrium phenomena, there is an increasing focus on going beyond conventional scenarios of thermalization. Traditionally examples of nonthermalizing systems are either integrable or disordered. Recently, examples of translationally invariant physical systems have been discovered whose excited energies avoid thermalization either due to local constraints (whether exact or emergent) or due to higher-form symmetries. In this article, we extend these investigations for the case of 3D U ( 1 ) quantum dimer models, which are lattice gauge theories with finite-dimensional local Hilbert spaces (also generically called quantum link models) with staggered charged static matter. Using a combination of analytical and numerical methods, we uncover a class of athermal states that arise in large winding sectors, when the system is subjected to external electric fields. The polarization of the dynamical fluxes in the direction of applied field traps excitations in 2D planes, while an interplay with the Gauss law constraint in the perpendicular direction causes exotic athermal behavior due to the emergence of new conserved quantities. This causes a geometric fragmentation of the system. We provide analytical arguments showing that the scaling of the number of fragments is exponential in the linear system size, leading to weak fragmentation. Further, we identify sectors which host fractonic excitations with severe mobility restrictions. The unitary evolution of fragments dominated by fractons is qualitatively different from the one dominated by nonfractonic excitations.
Abstract Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a suitable playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Our results reveal the single vison excitations inside the Z2 quantum spin liquid (QSL) and its condensation towards the 12×12\sqrt{12}\times \sqrt{12}12​×12​ 12 × 12 valence bond solid (VBS), and demonstrate the translational symmetry fractionalization and emergent O(4) symmetry at the QSL-VBS transition. We find the single vison excitations, whose convolution qualitatively reproduces the dimer spectra, are not free but subject to interaction effects throughout the transition. The nature of the VBS with its O(4) order parameters are unearthed in full scope. Our approach opens the avenue for generic solution of the static and dynamic properties of QDMs and has relevance towards the realization and detection of fractional excitations in programmable quantum simulators.