arXiv subjects

Michael Pretko

Publications and source records attributed to Michael Pretko.

At least 19 recordsLinked to original sources

arXiv2021

Fractons from polarons

Fractons are a type of emergent quasiparticle which cannot move freely in isolation, but can easily move in bound pairs. Similar phenomenology is found in boson-affected hopping models, encountered in the study of polaron systems and hole-doped Ising antiferromagnets, in which motion of a particle requires the creation or absorption of bosonic excitations. We show that boson-affected hopping models can provide a natural realization of fractons, either approximately or exactly, depending on the details of the system. We first consider a generic one-dimensional boson-affected hopping model, in which we show that single particles move only at sixth order in perturbation theory, while motion of bound states occurs at second order, allowing for a broad parameter regime exhibiting approximate fracton phenomenology. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment via integrating out the mediating bosons. We then consider a special type of boson-affected hopping models with mutual hard-core repulsion between particles and bosons, accessible in hole-doped mixed-dimensional Ising antiferromagnets, in which the hole motion is one dimensional in an otherwise two-dimensional antiferromagnetic background. We show that this system, which is within the current reach of ultracold-atom experiments, exhibits perfect fracton behavior to all orders in perturbation theory, thereby enabling the experimental study of dipole-conserving field theories. We further discuss diagnostic signatures of fractonic behavior in these systems. In studying these models, we also identify simple effective one-dimensional microscopic Hamiltonians featuring perfect fractonic behavior, paving the way to future studies on fracton physics in lower dimensions.

cond-mat.str-el↗

arXiv2020

Fractons from frustration in hole-doped antiferromagnets

Recent theoretical research on tensor gauge theories led to the discovery of an exotic type of quasiparticles, dubbed fractons, that obey both charge and dipole conservation. Here we describe physical implementation of dipole conservation laws in realistic systems. We show that fractons find a natural realization in hole-doped antiferromagnets. There, individual holes are largely immobile, while dipolar hole pairs move with ease. First, we demonstrate a broad parametric regime of fracton behavior in hole-doped two-dimensional Ising antiferromagnets viable through five orders in perturbation theory. We then specialize to the case of holes confined to one dimension in an otherwise two-dimensional antiferromagnetic background, which can be realized via the application of external fields in experiments, and prove ideal fracton behavior. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment. Manifestations of fractonicity in these systems include gravitational clustering of holes. We also discuss diagnostics of fracton behavior, which we argue is borne out in existing experimental results.

cond-mat.str-el↗

arXiv2020

Odd Fracton Theories, Proximate Orders, and Parton Constructions

The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy non-trivial conditions on their low-energy properties when a combination of lattice translation and $U(1)$ symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other sub-dimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that "odd" versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd $Z_2$ gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry-breaking, thereby allowing us to identify a class of conventional ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. Condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.

cond-mat.str-el↗

arXiv2020

Fractons from confinement in one dimension

Recent work has shown that two seemingly different physical mechanisms, namely fracton behavior and confinement, can give rise to non-ergodicity in one-dimensional quantum many-body systems. In this work, we demonstrate an intrinsic link between these two mechanisms by studying the dynamics of one-dimensional confining theories, such as a U(1) gauge theory and a quantum Ising model. We show that, within certain parameter regimes, these models exhibit effective fracton dynamics, characterized by immobility of stable single-particle excitations and free motion of dipolar bound states. By perturbatively integrating out the linearly confining field, we obtain an effective fracton Hamiltonian for the confined charges which exhibits conservation of dipole moment. We discuss an intuitive understanding of these results in terms of the motion of the confining strings, leading to potential extensions to higher dimensions. We thereby interpret recent observations of nonthermal eigenstates and glassy dynamics in confining theories in terms of corresponding results in the fracton literature.

cond-mat.str-el↗

arXiv2020

Fracton Phases of Matter

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.

cond-mat.str-el↗

arXiv2019

Crystal-to-Fracton Tensor Gauge Theory Dualities

We demonstrate several explicit duality mappings between elasticity of two-dimensional crystals and fracton tensor gauge theories, expanding on recent works by two of the present authors. We begin by dualizing the quantum elasticity theory of an ordinary commensurate crystal, which maps directly onto a fracton tensor gauge theory, in a natural tensor analogue of the conventional particle-vortex duality transformation of a superfluid. The transverse and longitudinal phonons of a crystal map onto the two gapless gauge modes of the tensor gauge theory, while the topological lattice defects map onto the gauge charges, with disclinations corresponding to isolated fractons and dislocations corresponding to dipoles of fractons. We use the classical limit of this duality to make new predictions for the finite-temperature phase diagram of fracton models, and provide a simpler derivation of the Halperin-Nelson-Young theory of thermal melting of two-dimensional solids. We extend this duality to incorporate bosonic statistics, which is necessary for a description of the quantum melting transitions. We thereby derive a hybrid vector-tensor gauge theory which describes a supersolid phase, hosting both crystalline and superfluid orders. The structure of this gauge theory puts constraints on the quantum phase diagram of bosons, and also leads to the concept of symmetry enriched fracton order. We formulate the extension of these dualities to systems breaking time-reversal symmetry. We also discuss the broader implications of these dualities, such as a possible connection between fracton phases and the study of interacting topological crystalline insulators.

cond-mat.str-el↗

arXiv2019

Electric Circuit Realizations of Fracton Physics

We design a set of classical macroscopic electric circuits in which charge exhibits the mobility restrictions of fracton quasiparticles. The crucial ingredient in these circuits is a transformer, which induces currents between pairs of adjacent wires. For an appropriately designed geometry, this induction serves to enforce conservation of dipole moment. We show that a network of capacitors connected via ideal transformers will forever remember the dipole moment of its initial charge configuration. Relaxation of the dipole moment in realistic systems can only occur via flux leakage in the transformers, which will lead to violations of fracton physics at the longest times. We propose a concrete diagnostic for these "fractolectric" circuits in the form of their characteristic equilibrium charge configurations, which we verify using simple circuit simulation software. These circuits not only provide an experimental testing ground for fracton physics, but also serve as DC filters. We outline extensions of these ideas to circuits featuring other types of higher moment conservation laws, as well as to higher-dimensional circuits which act as fracton "current-ice." While our focus is on classical circuits, we discuss how these ideas can be straightforwardly extended to realize quantized fractons in superconducting circuits.

cond-mat.str-el↗

arXiv2019

Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist, can potentially inhibit the condensation of vortices and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by proliferation of spinon dipoles. For example, we argue that a $2d$ VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long range entanglement. Such a bond liquid phase yields a concrete example of the elusive $2d$ Bose metal with symmetry fractionalization. We also study $3d$ valence plaquette and valence cube ordered phase, and demonstrate that the topological defects therein also have fractonic dynamics. Possible nearby phases after melting the valence plaquettes or cubes are also discussed.

cond-mat.str-el↗

arXiv2019

Symmetric Tensor Gauge Theories on Curved Spaces

Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of symmetric tensor gauge theories, which feature conservation laws restricting the motion of particles to lower-dimensional sub-spaces, such as lines or points. In this work, we investigate the fate of symmetric tensor gauge theories in the presence of spatial curvature. We find that weak curvature can induce small (exponentially suppressed) violations on the mobility restrictions of charges, leaving a sense of asymptotic fractonic/sub-dimensional behavior on generic manifolds. Nevertheless, we show that certain symmetric tensor gauge theories maintain sharp mobility restrictions and gauge invariance on certain special curved spaces, such as Einstein manifolds or spaces of constant curvature.

cond-mat.str-el↗

arXiv2019

The Fracton Gauge Principle

A powerful mechanism for constructing gauge theories is to start from a theory with a global symmetry, then apply the "gauge principle," which demands that this symmetry hold locally. For example, the global phase rotation of a system of conserved charges can be promoted to a local phase rotation by coupling to an ordinary U(1) vector gauge field. More recently, a class of particles has been studied featuring not only charge conservation, but also conservation of higher moments, such as dipole moment, which leads to severe restrictions on the mobility of charges. These particles, called fractons, are known to be intimately connected to symmetric tensor gauge fields. In this work, we show how to derive such tensor gauge theories by applying the gauge principle to a theory of ungauged fractons. We begin by formulating a field theory for ungauged fractons exhibiting global conservation of charge and dipole moment. We show that such fracton field theories have a characteristic non-Gaussian form, reflecting the fact that fractons intrinsically interact with each other even in the absence of a mediating gauge field. We then promote the global higher moment conservation laws to local ones, which requires the introduction of a symmetric tensor gauge field. Finally, we extend these arguments to other types of subdimensional particles besides fractons. This work offers a possible route to the formulation of non-abelian fracton theories.

cond-mat.str-el↗

arXiv2019

Dynamical scar states in driven fracton systems

One-dimensional fracton systems can exhibit perfect localization, failing to reach thermal equilibrium under arbitrary local unitary time evolution. We investigate how this nonergodic behavior manifests in the dynamics of a driven fracton system, specifically a one-dimensional Floquet quantum circuit model featuring conservation of a U(1) charge and its dipole moment. For a typical basis of initial conditions, a majority of states heat up to a thermal state at near-infinite temperature. In contrast, a small number of states flow to a localized steady state under the Floquet time evolution. We refer to these athermal steady states as ``dynamical scars," in analogy with the scar states observed in the spectra of certain many-body Hamiltonians. Despite their small number, these dynamical scars are experimentally relevant due to their high overlap with easily-prepared product states. Each scar state displays a single agglomerated fracton peak, in agreement with the steady-state configurations of fractonic random circuits. The details of these scars are insensitive to the precise form of the Floquet operator, which is constructed from random unitary matrices. Rather, dynamical scar states arise directly from fracton conservation laws, providing a concrete mechanism for the appearance of scars in systems with constrained quantum dynamics.

cond-mat.stat-mech↗

arXiv2019

Localization in fractonic random circuits

We study the spreading of initially-local operators under unitary time evolution in a 1d random quantum circuit model which is constrained to conserve a $U(1)$ charge and its dipole moment, 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 nontrivial predictions in good agreement with numerics. Importantly, these equations also predict localization in 2d fractonic circuits. Immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct to non-fractonic circuits. 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 follows semi-Poisson statistics, similar to eigenstates of MBL systems. The non-ergodic phenomenology persists to initial conditions containing non-zero density of dipolar or fractonic charge. Our work implies that low-dimensional fracton systems preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that 1d and 2d fracton systems should realize true MBL under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in d>1 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.

cond-mat.stat-mech↗

arXiv2019

On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective

Despite the seeming simplicity of the theory, calculating (and even defining) entanglement entropy for the Maxwell theory of a $U(1)$ gauge field in (3+1) dimensions has been the subject of controversy. It is generally accepted that the ground state entanglement entropy for a region of linear size $L$ behaves as an area law with a subleading logarithm, $S = αL^2 -γ\log L$. While the logarithmic coefficient $γ$ is believed to be universal, there has been disagreement about its precise value. After carefully accounting for subtle boundary corrections, multiple analyses in the high energy literature have converged on an answer related to the conformal trace anomaly, which is only sensitive to the local curvature of the partition. In contrast, a condensed matter treatment of the problem yielded a topological contribution which is not captured by the conformal field theory calculation. In this perspective piece, we review aspects of the various calculations and discuss the resolution of the discrepancy, emphasizing the important role played by charged states (the "extended Hilbert space") in defining entanglement for a gauge theory. While the trace anomaly result is sufficient for a strictly pure gauge field, coupling the gauge field to dynamical charges of mass $m$ gives a topological contribution to $γ$ which survives even in the $m\rightarrow\infty$ limit. For many situations, the topological contribution from dynamical charges is physically meaningful and should be taken into account. We also comment on other common issues of entanglement in gauge theories, such as entanglement distillation, algebraic definitions of entanglement, and gauge-fixing procedures.

hep-th↗

arXiv2019

Unitary-projective entanglement dynamics

Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low (i.e. area law) entanglement, in contrast with the volume law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area law entanglement for any measurement rate, as seen in certain non-interacting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law and critical 'fixed points.' We also discuss Floquet random circuits, where the answers depend on the order of limits - one order of limits yields area law entanglement for any non-zero measurement rate, whereas a different order of limits allows for an area law - volume law transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase. Note: The results presented here supersede those of all previous versions of this manuscript, which contained some erroneous claims.

cond-mat.stat-mech↗

arXiv2019

Symmetry Enriched Fracton Phases from Supersolid Duality

Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.

cond-mat.str-el↗

arXiv2018

Localization of Extended Quantum Objects

A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and membranes, arguing that such a system can also exhibit localization in the presence of sufficiently strong disorder (randomness) in the Hamiltonian. We show that localization of large extended objects can be mapped to a lower-dimensional many-body localization problem. For example, motion of a string involves propagation of point-like signals down its length to keep the different segments in causal contact. For sufficiently strong disorder, all such internal modes will exhibit many-body localization, resulting in the localization of the entire string. The eigenstates of the system can then be constructed perturbatively through a convergent 'string locator expansion.' We propose a type of out-of-time-order string correlator as a diagnostic of such a string localized phase. Localization of other higher-dimensional objects, such as membranes, can also be studied through a hierarchical construction by mapping onto localization of lower-dimensional objects. Our arguments are 'asymptotic' ($i.e.$ valid up to rare regions) but they extend the notion of localization (and localization protected order) to a host of settings where such ideas previously did not apply. These include high-dimensional ferromagnets with domain wall excitations, three-dimensional topological phases with loop-like excitations, and three-dimensional type-II superconductors with flux line excitations. In type-II superconductors, localization of flux lines could stabilize superconductivity at energy densities where a normal state would arise in thermal equilibrium.

cond-mat.stat-mech↗

arXiv2018

Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate

Deconfined quantum critical points are characterized by the presence of an emergent gauge field and exotic fractionalized particles, which exist as well-defined excitations only at the critical point. We here demonstrate the existence of quantum critical points described by an emergent tensor gauge theory featuring subdimensional excitations, in close relation to fracton theories. We begin by reexamining a previously studied deconfined quantum critical point between two valence bond solid (VBS) phases on a bilayer honeycomb lattice. We show that the critical theory maps onto a rank-two tensor gauge theory featuring one-dimensional particles. In a slightly different context, the same tensor gauge theory also describes a deconfined quantum critical point between a two-dimensional superfluid and a finite-momentum Bose condensate, both of which are dual to rank-one gauge theories. This represents an entirely new class of deconfined quantum criticality, in which a critical tensor gauge theory arises on top of a stable conventional gauge theory. Furthermore, we propose that this quantum critical point gives rise to a new finite-temperature phase of bosons, behaving as an exciton Bose condensate, in which excitons (boson-hole pairs) are condensed but individual bosons are not. We discuss how small modifications of this theory give rise to the stable quantum "exciton Bose liquid" phase studied by Paramekanti, Balents, and Fisher.

cond-mat.str-el↗

arXiv2018

Fracton-Elasticity Duality

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

cond-mat.str-el↗