Hilbert space fragmentation produces an effective attraction between fractons

Feng, Xiaozhou; Skinner, B. F.

doi:10.1103/physrevresearch.4.013053

Cited by 17 publications

(10 citation statements)

References 43 publications

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“…In strongly fragmented systems, the Krylov-Restricted Thermalization within the nonlocally constrained Krylov subspaces K j can lead to many surprising consequences, including atypical late-time expectation values of local operators [19,178], and an apparent Casimir effect [189]. For example, the infinite-temperature charge density profile within a Krylov subspace of the pair-hopping model of Eq.…”

Section: Krylov-restricted Thermalizationmentioning

confidence: 99%

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

2022

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The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom simulators and in the Aﬄeck-Kennedy-Lieb-Tasaki (AKLT) spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert Space Fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.

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Section: Krylov-restricted Thermalizationmentioning

confidence: 99%

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

2022

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“…as the unique solution. The polynomial 𝑦 3 − 3𝑥 2 𝑦 can also be included in the multipole group (31) without changing the fundamental solution (32). If 𝑦 3 − 3𝑥 2 𝑦 is instead the only third-order polynomial in the multipole group, then the allowed gates are no longer unique; the same two solutions are permitted as for the set of multipole moments in Eq.…”

Section: Triangular Latticementioning

confidence: 99%

“…[11] that imposing multipole symmetries on quantum dynamics could give rise to ergodicity breaking. This was later explained in terms of Hilbert space shattering/fragmentation [12][13][14], a phenomenon that has been observed experimentally [15,16], which could be harnessed for both quantum memories [12] and metrology [17], and which has been undergoing intensive exploration [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In a third development, it was realized in Refs.…”

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confidence: 99%

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Bulmash¹,

Hart²,

Nandkishore³

2023

Preprint

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Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the kagome and breathing kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct an effective Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two seemingly novel phenomena, including an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices. CONTENTS 3. Discussion D. Vector conserved quantities 1. Lattice Hamiltonian 2. Discussion V. Conclusions A. Group theory A.1. Irreducible representations of D 𝑀 A.2. Sorting polynomials into irreps A.3. Clebsch-Gordon coefficients for D 𝑀 B. Vector charge theory C. Discrete vs continuous translations D. From discrete derivatives to spin Hamiltonians D.1. Bravais lattice D.2. Introducing a basis D.3. Additional symmetries D.4. More general Hamiltonians E. Haar-random circuits and automaton dynamics References I. INTRODUCTIONMultipole symmetries have become a major topic of interest in condensed matter physics, quantum dynamics, and quantum information. This began with the work of Pretko [1] identifying conserved multipole moments as underlying the

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“…In order to identify the critical filling, we first study how the size of the symmetry sector scales with L and n. For this question we can exploit an exact analogy between the number of states in the symmetry sector and the number of non-decreasing lattice paths in a square grid that enclose a fixed area. The key idea is that one can define a "height field" y(x) defined for discrete values x by y(x) = w≤x n w [46,52]. This height field has an endpoint y(L − 1) = N that is fixed by the total charge, and an area under the curve x y(x) = N (L − 1) − P that is fixed by the dipole moment.…”

Section: B Size Of the Symmetry Sectormentioning

confidence: 99%

Exact solution for the filling-induced thermalization transition in a 1D fracton system

Pozderac,

Speck,

Feng

et al. 2022

Preprint

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We study a random circuit model of constrained fracton dynamics, in which particles on a onedimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density nc. Specifically, when evolution proceeds by operators that act on contiguous sites, the critical density is given by nc = 1/( − 2). We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent ν = 2. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: z = 4, while at the critical point it increases to zc 6.

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Hilbert space fragmentation produces an effective attraction between fractons

Cited by 17 publications

References 43 publications

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Exact solution for the filling-induced thermalization transition in a 1D fracton system

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