Finite-temperature screening of 
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(1) fractons

Pretko, Michael

doi:10.1103/physrevb.96.115102

Cited by 49 publications

(69 citation statements)

References 33 publications

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“…Fracton phases are also known to exhibit glassy dynamics. These have been studied [26,[54][55][56][57] for fracton systems in three spatial dimensions, using techniques akin to locator expansions. At non-zero densities and long enough times, "locator expansion" type techniques fail to converge, likely indicating thermalization at long times.…”

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confidence: 99%

Localization in Fractonic Random Circuits

2019

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We study the spreading of initially-local operators under unitary time evolution in a onedimensional random quantum circuit model which is constrained to conserve a U (1) charge and also the dipole moment of this charge. These constraints are motivated by the quantum dynamics of fracton phases. We discover that charge remains localized at its initial position, providing a crisp example of a non-ergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well-described by a system of coupled hydrodynamic equations, which makes several non-trivial predictions which are all in good agreement with numerics in one dimension. Importantly, these equations also predict localization in two-dimensional fractonic random circuits. We further find that the immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct from those observed in non-fractonic circuits. These non-standard exponents are also explained by our coupled hydrodynamic equations. Where entanglement properties are concerned, we find that fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum is found to follow semi-Poisson statistics, similar to eigenstates of many-body localized systems. The non-ergodic phenomenology is found to persist to initial conditions containing non-zero density of dipolar or fractonic charge, including states near the sector of maximal charge. Our work implies that low-dimensional fracton systems should preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that one-and two-dimensional fracton systems should realize true many-body localization (MBL) under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in spatial dimensions greater than one being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new non-ergodic phases in high dimensions.

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confidence: 99%

Localization in Fractonic Random Circuits

2019

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“…A second distinction from the 3d thermal liberation of intrinsic fractons described in Ref. [32], is that thermal screening of 3d fractons results in weaker power-law interactions, and whereas the dislocations continue to exhibit logarithmic confinement, up until a BKT transition, as described by the Halperin-Nelson theory.…”

Section: Super-nematic To Super-fluid Transitionmentioning

confidence: 90%

“…A detailed discussion of the finite temperature physics of fractonic matter was presented in Ref. [32]. The basic point is that fractons are only prevented from moving at zero temperature, where each forbidden move requires exciting additional gapped fracton excitations.…”

Section: Super-nematic To Super-fluid Transitionmentioning

confidence: 99%

Symmetry-enforced fractonicity and two-dimensional quantum crystal melting

Kumar

Potter

2019

Phys. Rev. B

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Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement. Here, we introduce the concept of symmetry enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence. A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation. Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for the symmetry enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions. We show that, at zero temperature, sufficiently strong quantum fluctuations of the crystal lattice favor the formation of a super-solid phase that spontaneously breaks the symmetry enforcing fractonicity of defects. The defects can then condense to drive the crystal into a super-nematic phase via a phase transition in the 2 + 1d XY universality class to drive a melting phase transition of the crystal to a nematic phase. This scenario contrasts the standard Halperin-Nelson scenario for thermal melting of 2d solids in which dislocations can proliferate via a single continuous thermal phase transition. We comment on the application of these results to other scenarios such as vortex lattice melting at a magnetic field induced superconductor-insulator transition, and quantum melting of charge density waves of stripes in a metal. arXiv:1808.05621v2 [cond-mat.str-el]

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“…Such a scenario is a manifestation of glassy dynamics, or "asymptotic localization" [100]. For the U (1) theories, featuring long-range interactions between fractons, this slow dynamics also manifests in a delayed onset of screening [101].…”

Section: A Glassy Dynamics Of Fractonsmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

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Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization.The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories.We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation.Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.

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Finite-temperature screening of U (1) fractons

Cited by 49 publications

References 33 publications

Localization in Fractonic Random Circuits

Localization in Fractonic Random Circuits

Symmetry-enforced fractonicity and two-dimensional quantum crystal melting

Fracton phases of matter

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