arXiv subjects

Brian Swingle

Publications and source records attributed to Brian Swingle.

At least 145 records · Page 8Linked to original sources

arXiv2013

A simple model of many-body localization

We study a simple and tractable model of many-body localization. The main idea is to take a renormalization group perspective in which local entanglement is removed to reach a product state. The model is built from a random local unitary which implements a real space renormalization procedure and a fixed point Hamiltonian with random exponentially decaying interactions. We prove that every energy eigenstate is localized, that energy is not transported, and argue that despite being fine tuned, the model is stable to perturbations. We also show that every energy eigenstate obeys an area law for entanglement entropy and we consider the dynamics of entanglement entropy under perturbations. In the case of extensive pertubations we recover a logarithmic growth of entanglement observed in recent numerical simulations.

cond-mat.dis-nn↗

arXiv2013

A signature of quantum spin liquids in superconductors with topological order

This paper has been withdrawn and superseded by a new version entitled "Singularity of the London penetration depth at quantum critical points in superconductors" by Debanjan Chowdhury, Brian Swingle, Erez Berg and Subir Sachdev, posted in arXiv:1305.2918. The more recent paper has a number of new interesting results and includes a comprehensive analysis of 3 different classes of QCPs, including the one that was originally considered.

cond-mat.str-el↗

arXiv2013

Energy trapping from Hagedorn densities of states

In this note, we construct simple stochastic toy models for holographic gauge theories in which distributions of energy on a collection of sites evolve by a master equation with some specified transition rates. We build in only energy conservation, locality, and the standard thermodynamic requirement that all states with a given energy are equally likely in equilibrium. In these models, we investigate the qualitative behavior of the dynamics of the energy distributions for different choices of the density of states for the individual sites. For typical field theory densities of states (\log(ρ(E)) ~ E^{α<1}), the model gives diffusive behavior in which initially localized distributions of energy spread out relatively quickly. For large N gauge theories with gravitational duals, the density of states for a finite volume of field theory degrees of freedom typically includes a Hagedorn regime (\log(ρ(E)) ~ E). We find that this gives rise to a trapping of energy in subsets of degrees of freedom for parametrically long time scales before the energy leaks away. We speculate that this Hagedorn trapping may be part of a holographic explanation for long-lived gravitational bound states (black holes) in gravitational theories.

hep-th↗

arXiv2013

Structure of entanglement in regulated Lorentz invariant field theories

Regulated Lorentz invariant quantum field theories satisfy an area law for the entanglement entropy $S$ of a spatial subregion in the ground state in $d>1$ spatial dimensions; nevertheless, the full density matrix contains many more than $e^{S}$ non-zero eigenvalues. We ask how well the state of a subregion $R$ in the ground state of such a theory can be approximated when keeping only the $e^{S}$ largest eigenvalues of the reduced density matrix of $R$. We argue that by taking the region $R$ big enough, we can always ensure that keeping roughly $e^{S}$ states leads to bounded error in trace norm even for subregions in gapless ground states. We support these general arguments with an explicit computation of the error in a half-space geometry for a free scalar field in any dimension. Along the way we show that the Renyi entropy of a ball in the ground state of any conformal field theory at small Renyi parameter is controlled by the conventional \textit{thermal entropy density} at low temperatures. We also reobtain and generalize some old results relevant to DMRG on the decay of Schmidt coefficients of intervals in one dimensional ground states. Finally, we discuss the role of the regulator, the insensitivity of our arguments to the precise ultraviolet physics, and the role of adiabatic continuity in our results.

cond-mat.stat-mech↗

arXiv2012

Oscillating terms in the Renyi entropy of Fermi liquids

In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and Fermi liquids corresponding to $2k_F$-like oscillations. Our theoretical tools are the one dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface. We compare this term to numerical calculations of entanglement using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find excellent agreement up to moderate interaction strengths.

cond-mat.str-el↗

arXiv2012

Constructing holographic spacetimes using entanglement renormalization

We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large $N$ limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large $N$ limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large $N$ theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).

hep-th↗

arXiv2012

Interplay between short and long-range entanglement in symmetry protected phases

We study a variety of questions related to entanglement in symmetry protected phases, especially those introduced in arXiv:1106.4772 (Chen et al., 2011). These phases are analogous to topological insulators in that they are short range entangled states with symmetry protected edge or surface states. We show that the now standard bulk-edge correspondence relating the entanglement spectrum to the gapless edge spectrum holds for these phases as well. We also consider the question of coupling these models to gauge fields or equivalently of introducing long range entanglement. We argue that this procedure yields models with perturbatively stable edge or surface states at a variety of interface types. The non-onsite nature of the edge symmetry plays an important role in our considerations.

cond-mat.str-el↗

arXiv2012

Entanglement sum rules in exactly solvable models

We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full system is the sum of the entropies of the two components. In the context of the exactly solvable models we consider, this result applies to the full entropy, but more generally it is a statement about the additivity of universal terms in the entropy. We also prove that the Renyi entropy is exactly additive and hence that the entanglement spectrum factorizes. Our proof simultaneously extends and simplifies previous arguments, with extensions including new models at zero temperature as well as the ability to treat finite temperature crossovers. We emphasize that while the additivity is an exact statement, each term in the sum may still be difficult to compute. Our results apply to a wide variety of phases including Fermi liquids, spin liquids, and some non-Fermi liquid metals.

cond-mat.str-el↗

arXiv2012

Experimental signatures of 3d fractional topological insulators

In this work we explore experimental signatures of fractional topological insulators in three dimensions. These are states of matter with a fully gapped bulk that host exotic gapless surface states and fractionally charged quasiparticles. They are partially characterized by a non-trivial magneto-electric response while preserving time reversal. We describe how these phases appear in a variety of probes including photoemmission, tunneling, and quantum oscillations. We also discuss the effects of doping and proximate superconductivity. We argue that despite our current theoretical inability to predict materials where such phases will realized, they should be relatively easy to detect experimentally.

cond-mat.str-el↗

arXiv2012

Area law violations in a supersymmetric model

We study the structure of entanglement in a supersymmetric lattice model of fermions on certain types of decorated graphs with quenched disorder. In particular, we construct models with controllable ground state degeneracy protected by supersymmetry and the choice of Hilbert space. We show that in certain special limits these degenerate ground states are associated with local impurities and that there exists a basis of the ground state manifold in which every basis element satisfies a boundary law for entanglement entropy. On the other hand, by considering incoherent mixtures or coherent superpositions of these localized ground states, we can find regions that violate the boundary law for entanglement entropy over a wide range of length scales. More generally, we discuss various desiderata for constructing violations of the boundary law for entanglement entropy and discuss possible relations of our work to recent holographic studies.

cond-mat.str-el↗

arXiv2012

Hidden Fermi surfaces in compressible states of gauge-gravity duality

General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, z, and a specific hyperscaling violation exponent, θ. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. (arXiv:1111.1023). We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.

cond-mat.str-el↗

arXiv2011

Universal crossovers between entanglement entropy and thermal entropy

We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition that the same low energy degrees of freedom which control low temperature thermal physics are also responsible for the long range entanglement in the quantum ground state. We demonstrate the correctness of the proposed scaling form and determine the scaling function for certain classes of gapless systems whose low energy physics is described by a conformal field theory. We also use our crossover formalism to argue that local systems which are "natural" can violate the boundary law at most logarithmically. In particular, we show that several non-Fermi liquid phases of matter have entanglement entropy that is at most of order $L^{d-1}\log{(L)} $ for a region of linear size $L$ thereby confirming various earlier suggestions in the literature. We also briefly apply our crossover formalism to the study of fluctuations in conserved quantities and discuss some subtleties that occur in systems that spontaneously break a continuous symmetry.

cond-mat.str-el↗

arXiv2011

Fractional Chern Insulators from the nth Root of Bandstructure

We provide a parton construction of wavefunctions and effective field theories for fractional Chern insulators. We also analyze a strong coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto the microsopic Hamiltonian. We show that this strong coupling expansion is useful because of a special hierarchy of energy scales in fractional quantum Hall physics. Our procedure is illustrated using the Hofstadter model and then applied to bosons at 1/2 filling and fermions at 1/3 filling in a checkerboard lattice model recently studied numerically. Because our construction provides a more or less unique mapping from microscopic model to effective parton description, we obtain wavefunctions in the same phase as the observed fractional Chern insulators without tuning any continuous parameters.

cond-mat.str-el↗

arXiv2011

Non-Abelian statistics versus the Witten anomaly

This paper is motivated by prospects for non-Abelian statistics of deconfined particle-like objects in 3+1 dimensions, realized as solitons with localized Majorana zeromodes. To this end, we study the fermionic collective coordinates of magnetic monopoles in 3+1 dimensional spontaneously-broken SU(2) gauge theories with various spectra of fermions. We argue that a single Majorana zeromode of the monopole is not compatible with cancellation of the Witten SU(2) anomaly. We also compare this approach with other attempts to realize deconfined non-Abelian objects in 3+1 dimensions.

hep-th↗

arXiv2011

Entanglement Structure of Deconfined Quantum Critical Points

We study the entanglement properties of deconfined quantum critical points. We show not only that these critical points may be distinguished by their entanglement structure but also that they are in general more highly entangled that conventional critical points. We primarily focus on computations of the entanglement entropy of deconfined critical points in 2+1 dimensions, drawing connections to topological entanglement entropy and a recent conjecture on the monotonicity under RG flow of universal terms in the entanglement entropy. We also consider in some detail a variety of issues surrounding the extraction of universal terms in the entanglement entropy. Finally, we compare some of our results to recent numerical simulations.

cond-mat.str-el↗

arXiv2011

A geometric proof of the equality between entanglement and edge spectra

The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand the physics of black holes, and we now apply them to determine the local structure of entanglement in quantum many-body systems.

cond-mat.str-el↗

arXiv2010

Mutual information and the structure of entanglement in quantum field theory

I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement structure of quantum field theories because it remains finite in the continuum limit. I argue that the mutual information has certain universal singularities that are a manifestation of the idea of "entanglement per scale". Moreover, I propose a method, based on an ansatz for higher dimensional twist operators, to compute the entanglement entropy, Renyi entropy, and mutual information in a general quantum field theory. The relevance of these results to the search for renormalization group monotones, to holographic duality, and to entanglement based simulation methods for many body systems are all discussed.

quant-ph↗

arXiv2010

Renyi entropy, mutual information, and fluctuation properties of Fermi liquids

I compute the leading contribution to the ground state Renyi entropy $S_α$ for a region of linear size $L$ in a Fermi liquid. The result contains a universal boundary law violating term simply related the more familiar entanglement entropy. I also obtain a universal crossover function that smoothly interpolates between the zero temperature result and the ordinary thermal Renyi entropy of a Fermi liquid. Formulas for the entanglement entropy of more complicated regions, including non-convex and disconnected regions, are obtained from the conformal field theory formulation of Fermi surface dynamics. These results permit an evaluation of the quantum mutual information between different regions in a Fermi liquid. I also study the number fluctuations in a Fermi liquid. Taken together, these results give a reasonably complete characterization of the low energy quantum information content of Fermi liquids.

cond-mat.str-el↗