arXiv subjects

Eduardo Fradkin

Publications and source records attributed to Eduardo Fradkin.

At least 37 records · Page 2Linked to original sources

arXiv2023

An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-$N$ technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii-Kosterlitz-Thouless phase transition in the clean limit at large $N$. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

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arXiv2023

Field Theoretic Aspects of Condensed Matter Physics: An Overview

In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown enormously with time, and Quantum Field Theory has become a central conceptual tool in Condensed Matter Physics. In this chapter I cover how these ideas and tools have influenced our understanding of phase transitions, both classical and quantum, as well as topological phases of matter, and dualities.

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arXiv2022

Theory of oblique topological insulators

A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional $Θ$-angles, long-range entanglement, and fractionalization. Starting from a simple family of $\mathbb{Z}_N$ lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons -- bound states of electric charges and monopoles -- condense, leading to FTI phases characterized by topological order, emergent one-form symmetries, and gapped boundary states not realizable in 2+1-D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal "generalized magnetoelectric effect" in the presence of two-form background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.

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arXiv2022

Magnetic-field sensitive charge density wave orders in the superconducting phase of UTe2

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-abelian Majorana modes, chiral supercurrents, and half-quantum vortices. However, fundamentally new, and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. In this work we use scanning tunneling microscopy to reveal an unusual charge density wave (CDW) order in the heavy fermion triplet superconductor, UTe2. Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity get weaker with increasing field, eventually disappearing at the superconducting critical field, Hc2. To explain the origin and phenomenology of this unusual CDW, we construct a Ginzburg-Landau theory for a uniform triplet superconductor coexisting with three triplet pair density wave (PDW) states. This theory gives rise to daughter CDWs which would be sensitive to magnetic field due to their origin in a triplet PDW state, and naturally explains our data. Our discovery of a CDW sensitive to magnetic fields and strongly intertwined with superconductivity, provides important new information for understanding the order parameter of UTe2 and uncovers the possible existence of a new kind of triplet PDW order which has not been previously explored.

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arXiv2022

Vortices in a Ginzburg Landau Theory of Superconductors with Nematic Order

In this work we explore the interplay between superconductivity and nematicity in the framework of a Ginzburg Landau theory with a nematic order parameter coupled to the superconductor order parameter, often used in the description of superconductivity of Fe based materials. In particular, we focus on the study of the vortex-vortex interaction in order to determine the way nematicity affects its attractive or repulsive character. To do so, we use a dynamical method based on the solutions of the Time Dependent Ginzburg Landau equations in a bulk superconductor. An important contribution of our work is the implementation of a pseudo-spectral method to solve the dynamics, known to be highly efficient and of very high order in comparison to the usual finite differences/elements methods. The coupling between the superconductor and the (real) nematic order parameters is represented by two terms in the free energy: a biquadratic term and a coupling of the nematic order parameter to the covariant derivatives of the superconductor order parameter. Our results show that there is a competing effect: while the former independently of its competitive or cooperative character generates an attractive vortex-vortex interaction, the latter always generates a repulsive interaction.

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arXiv2021

Thermalization of Randomly Coupled SYK Models

We investigate the thermalization of Sachdev-Ye-Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-$N$ limit. Using numerical large-$N$ methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-$N$ artifact by repeating the quench for finite $N$ and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the $N \to \infty$ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

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arXiv2021

Generic character of charge and spin density waves in superconducting cuprates

Understanding the nature of charge density waves (CDW) in cuprate superconductors has been complicated by material specific differences. A striking example is the opposite doping dependence of the CDW ordering wavevector in La-based and Y-based compounds, the two families where charge ordering is strongest and best characterized. Here we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La$_{1.8-x}$ Eu$_{0.2}$ Sr$_{x}$ CuO$_{4}$ over a range of doping $0.07 \leq x \leq 0.20$. For all dopings studied by RSXS, we find that the CDW amplitude is approximately temperature-independent and develops well above experimentally accessible temperatures. Surprisingly, the CDW ordering wavevector shows a non-monotonic temperature dependence, with a sudden change occurring at temperatures near the SDW onset temperature. We describe this behavior with a Landau-Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and CDW-SDW coupling. Our Landau-Ginzburg analysis suggests that the ordering wavevector at high temperatures decreases with increased doping. This behavior is opposite to the trend at low temperatures and highly reminiscent of the doping dependence seen in YBa$_2$ Cu$_3$ O$_{6+δ}$ , suggesting a common origin of the CDW in hole-doped cuprate superconductors.

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arXiv2021

Multiple charge density waves and superconductivity nucleation at antiphase domain walls in the nematic pnictide Ba$_{1-x}$Sr$_{x}$Ni$_{2}$As$_{2}$

How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba$_{1-x}$Sr$_{x}$Ni$_{2}$As$_{2}$ (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a six-fold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at $x_c=0.7$). The superconductivity is, however, anomalous, with the resistive transition for $0.4 < x< x_c$ occurring at a higher temperature than the specific heat anomaly. Using x-ray scattering, we discovered a new charge density wave (CDW) in BSNA in this composition range. The CDW is commensurate with a period of two lattice parameters, and is distinct from the two CDWs previously reported in this material. We argue that the anomalous transport behavior arises from heterogeneous superconductivity nucleating at antiphase domain walls in this CDW. We also present new data on the incommensurate CDW, previously identified as being unidirectional, showing that is a rotationally symmetric, "4$Q$" state with $C_4$ symmetry. Our study establishes BSNA as a rare material containing three distinct CDWs, and an exciting testbed for studying coupling between CDW, nematic, and SC orders.

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arXiv2020

A composite particle construction of the Fibonacci fractional quantum Hall state

The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $τ$, with fusion rule $τ\timesτ=1+τ$. While it has been proposed that the anyon spectrum of the $ν=12/5$ fractional quantum Hall state includes a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a quantum Hall system has been lacking. Here we use recently proposed non-Abelian dualities to construct a Fibonacci state of bosons at filling $ν=2$ starting from a trilayer of integer quantum Hall states. Our parent theory consists of bosonic "composite vortices" coupled to fluctuating $U(2)$ gauge fields, which is related to the standard theory of Laughlin quasiparticles by duality. The Fibonacci state is obtained by clustering the composite vortices between the layers, along with flux attachment, a procedure reminiscent of the clustering picture of the Read-Rezayi states. We further use this framework to motivate a wave function for the Fibonacci fractional quantum Hall state.

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arXiv2020

Non-Abelian Fermionization and the Landscape of Quantum Hall Phases

The recent proposal of non-Abelian boson-fermion dualities in 2+1 dimensions, which morally relate $U(k)_N$ to $SU(N)_{-k}$ Chern-Simons-matter theories, presents a new platform for exploring the landscape of non-Abelian quantum Hall states accessible from theories of Abelian composite particles. Here we focus on dualities relating theories of Abelian quantum Hall states of bosons or fermions to theories of non-Abelian "composite fermions" partially filling Landau levels. We show that these dualities predict special filling fractions where both Abelian and non-Abelian composite fermion theories appear capable of hosting distinct topologically ordered ground states, one Abelian and the other a non-Abelian, $U(k)_2$ Blok-Wen state. Rather than being in conflict with the duality, we argue that these results indicate unexpected dynamics in which the infrared and lowest Landau level limits fail to commute across the duality. In such a scenario, the non-Abelian topological order can be destabilized in favor of the Abelian ground state, suggesting the presence of a phase transition between the Abelian and non-Abelian states that is likely to be first order. We also generalize these constructions to other non-Abelian fermion-fermion dualities, in the process obtaining new derivations of a variety of paired composite fermion phases using duality, including the anti-Pfaffian state. Finally, we describe how, in multilayer constructions, excitonic pairing of the composite fermions across $N$ layers can also generate the family of Blok-Wen states with $U(k)_2$ topological order.

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arXiv2020

Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions

We investigate the problem of intertwined orders in fractional Chern insulators by considering lattice fractional quantum Hall (FQH) states arising from pairing of composite fermions in the square-lattice Hofstadter model. At certain filling fractions, magnetic translation symmetry ensures the composite fermions form Fermi surfaces with multiple pockets, leading to the formation of finite-momentum Cooper pairs in the presence of attractive interactions. We obtain mean-field phase diagrams exhibiting a rich array of striped and topological phases, establishing paired lattice FQH states as an ideal platform to investigate the intertwining of topological and conventional broken symmetry order.

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arXiv2020

Topology and the one-dimensional Kondo-Heisenberg model

The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes.

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arXiv2019

The Physics of Pair Density Waves

We review the physics of pair density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge density wave, and discuss related vestigial states that emerge as a consequence of partial meting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a "mother order" or another competing order in the cuprates. In addition, we give an overview of the weak coupling version of PDW order, Fulde-Ferrell-Larkin-Ovchinnikov states, in the context of cold atom systems, unconventional superconductors, and non-centrosymmetric and Weyl materials.

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arXiv2019

Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization

It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite particles. We show that progress on this problem can be made using recently proposed non-Abelian bosonization dualities in 2+1 dimensions, which morally relate $U(N)_k$ and $SU(k)_{-N}$ Chern-Simons-matter theories. The advantage of these dualities is that regions of the phase diagram which may be obscure on one side of the duality can be accessed by condensing local operators on the other side. Starting from parent Abelian states, we use this approach to construct Landau-Ginzburg theories of non-Abelian states through a pairing mechanism. In particular, we obtain the bosonic Read-Rezayi sequence at fillings $ν=k/(kM+2)$ by starting from $k$ layers of bosons at $ν=1/2$ with $M$ Abelian fluxes attached. The Read-Rezayi states arise when $k$-clusters of the dual non-Abelian bosons condense. We extend this construction by showing that $N_f$-component generalizations of the Halperin $(2,2,1)$ bosonic states have dual descriptions in terms of $SU(N_f+1)_1$ Chern-Simons-matter theories, revealing an emergent global symmetry in the process. Clustering $k$ layers of these theories yields a non-Abelian $SU(N_f)$-singlet state at filling $ν= kN_f / (N_f + 1 + kMN_f)$.

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arXiv2019

Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

The properties of the isotropic incompressible $ν=5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+ip_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $ν=5/2$. This finding motivates us to consider an inhomogeneous paired state - a $p_x+ip_y$ pair-density-wave (PDW) - whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and anti-domain walls of the $p_x+i p_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy $E_{F}$ and the PDW pairing energy $E_{\textrm{pdw}}$. The analysis of this interplay yields a rich set of topological states. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases - as well as transitions thereof - tuned by the strength of the paired liquid crystalline order.

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arXiv2018

Boson-fermion duality in a gravitational background

We study the $2+1$ dimensional boson-fermion duality in the presence of background curvature and electromagnetic fields. The main players are, on the one hand, a massive complex $|ϕ|^4$ scalar field coupled to a $U(1)$ Maxwell-Chern-Simons gauge field at level $1$, representing a relativistic composite boson with one unit of attached flux, and on the other hand, a massive Dirac fermion. We show that, in a curved background and at the level of the partition function, the relativistic composite boson, in the infinite coupling limit, is dual to a short-range interacting Dirac fermion. The coupling to the gravitational spin connection arises naturally from the spin factors of the Wilson loop in the Chern-Simons theory. A non-minimal coupling to the scalar curvature is included on the bosonic side in order to obtain agreement between partition functions. Although an explicit Lagrangian expression for the fermionic interactions is not obtained, their short-range nature constrains them to be irrelevant, which protects the duality in its strong interpretation as an exact mapping at the IR fixed point between a Wilson-Fischer-Chern-Simons complex scalar and a free Dirac fermion. We also show that, even away from the IR, keeping the $|ϕ|^4$ term is of key importance as it provides the short-range bosonic interactions necessary to prevent intersections of worldlines in the path integral, thus forbidding unknotting of knots and ensuring preservation of the worldline topologies.

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arXiv2018

Helical spin thermoelectrics controlled by a side-coupled magnetic quantum dot in the quantum spin Hall state

We study the thermoelectric response of a device containing a pair of helical edge states contacted at the same temperature $T$ and chemical potential $μ$ and connected to an external reservoir, with different chemical potential and temperature, through a side quantum dot. Different operational modes can be induced by applying a magnetic field $B$ and a gate voltage $V_g$ at the quantum dot. At finite $B$, the quantum dot acts simultaneously as a charge and a spin filter. Charge and spin currents are induced, not only through the quantum dot, but also along the edge states. We focus on linear response and analyze the regimes, which we identify as charge heat engines or refrigerator, spin heat engine and spin refrigerator.

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arXiv2018

Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions

Motivated by the appearance of a `reflection symmetry' in transport experiments and the absence of statistical periodicity in relativistic quantum field theories, we propose a series of relativistic composite fermion theories for the compressible states appearing at filling fractions $ν=1/2n$ in quantum Hall systems. These theories consist of electrically neutral Dirac fermions attached to $2n$ flux quanta via an emergent Chern-Simons gauge field. While not possessing an explicit particle-hole symmetry, these theories reproduce the known Jain sequence states proximate to $ν=1/2n$, and we show that such states can be related by the observed reflection symmetry, at least at mean field level. We further argue that the lowest Landau level limit requires that the Dirac fermions be tuned to criticality, whether or not this symmetry extends to the compressible states themselves.

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