arXiv subjects

Michael Pretko

Publications and source records attributed to Michael Pretko.

29 records · Page 2Linked to original sources

arXiv2018

Pinch Point Singularities of Tensor Spin Liquids

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U(1)$ gauge theories. These "higher rank" tensor models are particularly intriguing due to the presence of quasi-particles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch-point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional $U(1)$ spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.

cond-mat.str-el↗

arXiv2018

AC Conductivity Crossover in Localized Superconductors

An important experimental signature of localization is the low-frequency AC conductivity, which typically vanishes as $ω^ϕ$. The exponent $ϕ= 2$ for Anderson insulators, whereas for many body localized insulators $ϕ$ is a continuously varying exponent $1 \le ϕ\le 2$. In this work, we study the low-frequency AC conductivity of localized superconductors, in which disorder is strong enough to localize all quasiparticles, while remaining weak enough to leave superconductivity intact. We find that while the ac conductivity still follows the general form $σ(ω) \sim ω^ϕ$, the exponent $ϕ$ can be markedly different from the characteristic value for localized insulators. In particular, in certain symmetry classes at zero temperature, we obtain $ϕ> 2$. We further identify an interesting temperature dependent crossover in the scaling form of the AC conductivity, which could be useful for the experimental characterization of localized superconductors.

cond-mat.dis-nn↗

arXiv2018

Fractonic line excitations : an inroad from 3d elasticity theory

We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form gauge theories with symmetric tensor gauge theories, see direct physical realization as the topological lattice defects of ordinary three-dimensional quantum crystals. Starting with the more familiar elasticity theory, we show how it maps onto a rank-4 tensor gauge theory, with phonons corresponding to gapless gauge modes and disclination defects corresponding to line-like charges. We derive flux conservation laws which lock these line-like excitations in place, analogous to the higher moment charge conservation laws of fracton theories. This way of encoding mobility restrictions of lattice defects could shed light on melting transitions in three dimensions. This new type of extended object may also be a useful tool in the search for improved quantum error-correcting codes in three dimensions.

cond-mat.str-el↗

arXiv2018

Emergent Phases of Fractonic Matter

Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the "condensed matter" of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in "quantum Hall" states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies.

cond-mat.str-el↗

arXiv2017

Higher-Spin Witten Effect and Two-Dimensional Fracton Phases

We study the role of "$θ$ terms" in the action for three-dimensional $U(1)$ symmetric tensor gauge theories, describing quantum phases of matter hosting gapless higher-spin gauge modes and gapped subdimensional particle excitations, such as fractons. In Maxwell theory, the $θ$ term is a total derivative which has no effect on the gapless photon, but has two important, closely related consequences: attaching electric charge to magnetic monopoles (the Witten effect) and leading to a Chern-Simons theory on the boundary. We will find that a similar story holds in the higher-spin $U(1)$ gauge theories. These theories admit generalized $θ$ terms which have no effect on the gapless gauge mode, but which bind together electric and magnetic charges (both of which are generally subdimensional) in specific combinations, in a higher-spin manifestation of the Witten effect. We derive the corresponding Witten quantization condition. We find that, as in Maxwell theory, imposing time-reversal invariance restricts $θ$ to certain discrete values. We also find that these new $θ$ terms imply a non-trivial boundary structure. The boundaries host fracton excitations coupled to a tensor $U(1)$ gauge field with a Chern-Simons-like action, in both chiral and non-chiral varieties. These boundary theories open a door to the study of $U(1)$ fracton phases described by tensor Chern-Simons theories, not only on boundaries of three-dimensional systems, but also in strictly two spatial dimensions. We explicitly work through three examples of bulk and boundary theories, the principles of which can be readily extended to arbitrary higher-spin theories.

cond-mat.str-el↗

arXiv2017

Finite-Temperature Screening of U(1) Fractons

We investigate the finite-temperature screening behavior of three-dimensional U(1) spin liquid phases with fracton excitations. Several features are shared with the conventional U(1) spin liquid. The system can exhibit spin liquid physics over macroscopic length scales at low temperatures, but screening effects eventually lead to a smooth finite-temperature crossover to a trivial phase at sufficiently large distances. However, unlike more conventional U(1) spin liquids, we find that complete low-temperature screening of fractons requires not only very large distances, but also very long timescales. At the longest timescales, a charged disturbance (fracton) will acquire a screening cloud of other fractons, resulting in only short-range correlations in the system. At intermediate timescales, on the other hand, a fracton can only be partially screened by a cloud of mobile excitations, leaving weak power-law correlations in the system. Such residual power-law correlations may be a useful diagnostic in an experimental search for U(1) fracton phases.

cond-mat.str-el↗

arXiv2017

Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story

It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these theories couples naturally to subdimensional particles (such as fractons), which are restricted by gauge invariance to move only along lower-dimensional subspaces of the system. We here work out some of the basic generalized electromagnetic properties of subdimensional particles coupled to tensor electromagnetism, such as generalized electrostatic fields, potential formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some concepts from conventional electromagnetism will carry over directly, while others require significant modification.

cond-mat.str-el↗

arXiv2017

Entanglement Entropy of U(1) Quantum Spin Liquids

We here investigate the entanglement structure of the ground state of a (3+1)-dimensional U(1) quantum spin liquid, which is described by the deconfined phase of a compact U(1) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations of the system. It is found that, for a given bipartition of the system, the elements of the entanglement spectrum can be grouped according to the electric flux between the two regions, leading to a useful interpretation of the entanglement spectrum in terms of electric charges living on the boundary. The entanglement spectrum is also given additional structure due to the presence of the gapless photon. Making use of the Bisognano-Wichmann theorem and a local thermal approximation, these two contributions to the entanglement (particle and photon) are recast in terms of boundary and bulk contributions, respectively. Both pieces of the entanglement structure give rise to universal subleading terms (relative to the area law) in the entanglement entropy, which are logarithmic in the system size (log L), as opposed to the subleading constant term in gapped topologically ordered systems. The photon subleading logarithm arises from the low-energy conformal field theory and is essentially local in character. The particle subleading logarithm arises due to the constraint of closed electric loops in the wavefunction and is shown to be the natural generalization of topological entanglement entropy to the U(1) spin liquid. This contribution to the entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath construction (which generalizes the Kitaev-Preskill scheme to three dimensions).

cond-mat.str-el↗

arXiv2017

Nodal Line Entanglement Entropy: Generalized Widom Formula from Entanglement Hamiltonians

A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions. In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area law for entanglement entropy, as dictated by the Widom formula. We here generalize this formula to the case of arbitrary codimension, which is of particular interest for nodal lines in three dimensions. We first rederive the standard Widom formula by calculating an entanglement Hamiltonian for Fermi surface systems, obtained by repurposing a trick commonly applied to relativistic theories. The entanglement Hamiltonian will take a local form in terms of a low-energy patch theory for the Fermi surface, though it is nonlocal with respect to the microscopic fermions. This entanglement Hamiltonian can then be used to derive the entanglement entropy, yielding a result in agreement with the Widom formula. The method is then generalized to arbitrary codimension. For nodal lines, the area law is obeyed, and the magnitude of the coefficient for a particular partition is non-universal. However, the coefficient has a universal dependence on the shape and orientation of the nodal line relative to the partitioning surface. By comparing the relative magnitude of the area law for different partitioning cuts, entanglement entropy can be used as a tool for diagnosing the presence and shape of a nodal line in a ground state wavefunction.

cond-mat.str-el↗

arXiv2017

Emergent Gravity of Fractons: Mach's Principle Revisited

Recent work has established the existence of stable quantum phases of matter described by symmetric tensor gauge fields, which naturally couple to particles of restricted mobility, such as fractons. We focus on a minimal toy model of a rank 2 tensor gauge field, consisting of fractons coupled to an emergent graviton (massless spin-2 excitation). We show how to reconcile the immobility of fractons with the expected gravitational behavior of the model. First, we reformulate the fracton phenomenon in terms of an emergent center of mass quantum number, and we show how an effective attraction arises from the principles of locality and conservation of center of mass. This interaction between fractons is always attractive and can be recast in geometric language, with a geodesic-like formulation, thereby satisfying the expected properties of a gravitational force. This force will generically be short-ranged, but we discuss how the power-law behavior of Newtonian gravity can arise under certain conditions. We then show that, while an isolated fracton is immobile, fractons are endowed with finite inertia by the presence of a large-scale distribution of other fractons, in a concrete manifestation of Mach's principle. Our formalism provides suggestive hints that matter plays a fundamental role, not only in perturbing, but in creating the background space in which it propagates.

cond-mat.str-el↗

arXiv2017

Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids

Spin liquids are conventionally described by gauge theories with a vector gauge field. However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids. We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the "fracton" models recently discovered by Vijay, Haah, and Fu. Tensor gauge theories have more conservation laws than the simple charge conservation law of rank 1 theories. These conservation laws place severe restrictions on the motion of particles. Particles in some models are fully immobile (fractons), while other models have particles restricted to motion along lower-dimensional subspaces.

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