arXiv subjects

Erez Berg

Publications and source records attributed to Erez Berg.

At least 91 records · Page 5Linked to original sources

arXiv2021

Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States

We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with emergent symmetries of the edge, which play a crucial role in the structure of its phase diagram. Using this symmetry principle, transitions between distinct gapped phases at the boundaries of Abelian states can be understood in terms of symmetry breaking transitions or transitions between symmetry protected topological phases. Yet more exotic phenomena occur when the bulk hosts non-Abelian anyons. To demonstrate these principles, we explore the phase diagrams of the edges of a single and a double layer of the toric code, as well as those of domain walls in a single and double-layer Kitaev spin liquid (KSL). In the case of the KSL, we find that the presence of a non-Abelian anyon in the bulk enforces Kramers-Wannier self-duality as a symmetry of the effective boundary theory. These examples illustrate a number of surprising phenomena, such as spontaneous duality-breaking, two-sector phase transitions, and unfreezing of marginal operators at a transition between different gapless phases.

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arXiv2021

Converting electrons into emergent fermions at a superconductor-Kitaev spin liquid interface

We study an interface between a Kitaev spin liquid (KSL) in the chiral phase and a non-chiral superconductor. When the coupling across the interface is sufficiently strong, the interface undergoes a transition into a phase characterized by a condensation of a bound state of a Bogoliubov quasiparticle in the superconductor and an emergent fermionic excitation in the spin liquid. In the condensed phase, electrons in the superconductor can coherently convert into emergent fermions in the spin liquid and vice versa. As a result, the chiral Majorana edge mode of the spin liquid becomes visible in the electronic local density of states at the interface, which can be measured in scanning tunneling spectroscopy experiments. We demonstrate the existence of this phase transition, and the non-local order parameter that characterizes it, using density matrix renormalization group simulations of a KSL strip coupled at its edge to a superconductor. An analogous phase transition can occur in a simpler system composed of a one-dimensional spin chain with a spin-flip $\mathbb{Z}_2$ symmetry coupled to a superconductor.

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arXiv2021

Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained Sr$_2$RuO$_4$

Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van Hove singularity of the electronic spectrum crosses the Fermi energy, is expected to cause a change in the temperature dependence of the electrical resistivity from its Fermi liquid behavior $ρ\sim T^{2}$ to $ρ\sim T^{2}{\rm log}\left(1/T\right)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation originates from the same multi-band scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the strange metal Sr$_{3}$Ru$_{2}$O$_{7}$. In contrast, the thermal resistivity $ρ_{Q}\equiv T/κ$, where $κ$ is the thermal conductivity, is governed by qualitatively distinct processes that involve a broad continuum of compressive modes, i.e. long wavelength density excitations in Van Hove systems. While these compressive modes do not affect the charge current, they couple to thermal transport and yield $ρ_{Q}\propto T^{3/2}$. As a result, we predict that the Wiedemann-Franz law in strained Sr$_{2}$RuO$_{4}$ should be violated with a Lorenz ratio $L\propto T^{1/2}{\rm log}\left(1/T\right)$. We expect this effect to be observable in the temperature and strain regime where the anomalous charge transport was established.

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arXiv2021

The Hubbard Model

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.

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arXiv2021

Specific Heat of a Quantum Critical Metal

We investigate the specific heat, $c$, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where $c/T$ is close to the value expected from the non-interacting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of $c/T$, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of $c/T$ onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

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arXiv2021

Theory of Multi-Orbital Topological Superconductivity in Transition Metal Dichalcogenides

We study possible superconducting states in transition metal dichalcogenide (TMD) monolayers, assuming an on-site pairing potential that includes both intra- and inter-orbital terms. We find that if the mirror symmetry with respect to the system's plane is broken (e.g., by a substrate), this type of pairing can give rise to unconventional superconductivity, including time-reversal-invariant nodal and fully gapped topological phases. Using a multi-orbital renormalization group procedure, we show how these phases may result from the interplay between the local Coulomb repulsion, Hund's rule coupling, and phonon-mediated attraction. In particular, for a range of interaction parameters, the system transitions from a trivial phase to a nodal phase and finally to a gapped topological phase upon increasing the strength of the mirror symmetry breaking term.

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arXiv2021

Half and quarter metals in rhombohedral trilayer graphene

Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moiré superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moiré materials to be fundamentally itinerant in nature.

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arXiv2021

Strain-induced time reversal breaking and half quantum vortices near a putative superconducting tetra-critical point in Sr$_2$RuO$_4$

It has been shown [1] that many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for as resulting from the existence of an assumed tetra-critical point at near ambient pressure at which $d_{x^2-y^2}$ and $g_{xy(x^2-y^2)}$ superconducting states are degenerate. We perform both a Landau-Ginzburg and a microscopic mean-field analysis of the effect of spatially varying strain on such a state. In the presence of finite $xy$ shear strain, the superconducting state consists of two possible symmetry-related time-reversal symmetry (TRS) preserving states: $d \pm g$. However, at domain walls between two such regions, TRS can be broken, resulting in a $d+ig$ state. More generally, we find that various natural patterns of spatially varying strain induce a rich variety of superconducting textures, including half-quantum fluxoids. These results may resolve some of the apparent inconsistencies between the theoretical proposal and various experimental observations, including the suggestive evidence of half-quantum vortices [2]. [1] Steven A Kivelson, Andrew C Yuan, BJ Ramshaw, and Ronny Thomale, "A proposal for reconciling diverse experiments on the superconducting state in Sr$_2$RuO$_4$," npj Quantum Mater 5 (2020). [2] J Jang, DG Ferguson, V Vakaryuk, Raffi Budakian, SB Chung, PM Goldbart, and Y Maeno, "Observation of half-height magnetization steps in Sr$_2$RuO$_4$," Science 331, 186-188 (2011).

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arXiv2021

Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions -- density-density, spin exchange, and pair-hopping -- that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these sign-problem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field $J_1$-$J_2$ Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weak-coupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model.

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arXiv2021

Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators

We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of k-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum number, k. We moreover show that, when fully many-body localized, periodically driven systems of interacting fermions in two dimensions are characterized by a quantized magnetization in the bulk, thus confirming the quantization of magnetization of the anomalous Floquet insulator. We demonstrate our results with numerical simulations.

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arXiv2021

Spin-polarized superconductivity: order parameter topology, current dissipation, and multiple-period Josephson effect

We discuss transport properties of fully spin-polarized triplet superconductors, where only electrons of one spin component (along a certain axis) are paired. Due to the structure of the order parameter space, wherein phase and spin rotations are intertwined, a configuration where the superconducting phase winds by $4π$ in space is topologically equivalent to a configuration with no phase winding. This opens the possibility of supercurrent relaxation by a smooth deformation of the order parameter, where the order parameter remains non-zero at any point in space throughout the entire process. During the process, a spin texture is formed. We discuss the conditions for such processes to occur and their physical consequences. In particular, we show that when a voltage is applied, they lead to an unusual alternating-current Josephson effect whose period is an integer multiple of the usual Josephson period. These conclusions are substantiated in a simple time-dependent Ginzburg-Landau model for the dynamics of the order parameter. One of the potential applications of our analysis is for moiré systems, such as twisted bilayer and double bilayer graphene, where superconductivity is found in the vicinity of ferromagnetism.

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arXiv2020

Modeling unconventional superconductivity at the crossover between strong and weak electronic interactions

High-temperature superconductivity emerges in a host of different quantum materials, often in a region of the phase diagram where the electronic kinetic energy is comparable in magnitude with the electron-electron Coulomb repulsion. Describing such an intermediate-coupling regime has proven challenging, as standard perturbative approaches are inapplicable. Hence, it is of enormous interest to find models that are amenable to be solved using exact methods. While important advances have been made in elucidating the properties of one such minimal model -- the Hubbard model -- via numerical simulations, the infamous fermionic sign-problem significantly limits the accessible parameter space. Here, we employ Quantum Monte Carlo (QMC) methods to solve a multi-band version of the Hubbard model that does not suffer from the sign-problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free QMC studies, this model does not have pre-existing fine-tuned magnetic order, and thus treats superconducting, magnetic, and charge degrees of freedom on an equal footing. We find that, as the electron-electron repulsion increases, a dome of antiferromagnetic order emerges in the intermediate-coupling regime, accompanied by a metal-to-insulator crossover line. Superconductivity is found only near the antiferromagnetic quantum phase transition located on the metallic side of the magnetic dome. Across the antiferromagnetic quantum phase transition we find a change in the dynamical character of the magnetic fluctuations, from slow and overdamped in the metallic side to fast and propagating in the insulating side. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.

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arXiv2020

Superconducting fractional quantum Hall edges via repulsive interactions

We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupling to the superconductor is weak an energy gap is opened only in the presence of sufficiently strong attractive interactions between the edge modes, which do not commonly occur in solid state experimental realizations. We therefore investigate the possibility of obtaining a gapped phase by increasing the strength of the proximity coupling to the superconductor. To this end, we use an effective wire construction model for the quantum Hall liquid and employ renormalization group methods to obtain the phase diagram of the system. Surprisingly, at strong proximity coupling we find a gapped phase which is stabilized for sufficiently strong repulsive interactions in the bulk of the quantum Hall fluids. We furthermore identify a duality transformation that maps between the weak coupling and strong coupling regimes, and use it to show that the gapped phases in both regimes are continuously connected through an intermediate proximity coupling regime.

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arXiv2020

Isospin Pomeranchuk effect and the entropy of collective excitations in twisted bilayer graphene

In condensed matter systems, higher temperatures typically disfavors ordered phases leading to an upper critical temperature for magnetism, superconductivity, and other phenomena. A notable exception is the Pomeranchuk effect in 3He, in which the liquid ground state freezes upon increasing the temperature due to the large entropy of the paramagnetic solid phase. Here we show that a similar mechanism describes the finite temperature dynamics of spin and valley-isospins in magic-angle twisted bilayer graphene. Most strikingly a resistivity peak appears at high temperatures near superlattice filling factor nu = -1, despite no signs of a commensurate correlated phase appearing in the low-temperature limit. Tilted field magnetotransport and thermodynamic measurements of the inplane magnetic moment show that the resistivity peak is adiabatically connected to a finite-field magnetic phase transition at which the system develops finite isospin polarization. These data are suggestive of a Pomeranchuk-type mechanism, in which the entropy of disordered isospin moments in the ferromagnetic phase stabilizes it relative to an isospin unpolarized Fermi liquid phase at elevated temperatures. Measurements of the entropy, S/kB indeed find it to be of order unity per unit cell area, with a measurable fraction that is suppressed by an in-plane magnetic field consistent with a contribution from disordered physical spins. In contrast to 3He, however, no discontinuities are observed in the thermodynamic quantities across this transition. Our findings imply a small isospin stiffness, with implications for the nature of finite temperature transport as well as the mechanisms underlying isospin ordering and superconductivity in twisted bilayer graphene and related systems.

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arXiv2020

Low frequency Raman response near Ising-nematic quantum critical point: a memory matrix approach

Recent Raman scattering experiments have revealed a "quasi-elastic peak" in $\mathrm{FeSe_{1-x}S_x}$ near an Ising-nematic quantum critical point (QCP) \cite{zhang17}. Notably, the peak occurs at sub-temperature frequencies, and softens as $T^α$ when temperature is decreased toward the QCP, with $α>1$. In this work, we present a theoretical analysis of the low-frequency Raman response using a memory matrix approach. We show that such a quasi-elastic peak is associated with the relaxation of an Ising-nematic deformation of the Fermi surface. Specifically, we find that the peak frequency is proportional to $ τ^{-1}χ^{-1}$, where $χ$ is the Ising-nematic thermodynamic susceptibility, and $τ^{-1}$ is the decay rate of the nematic deformation due to an interplay between impurity scattering and electron-electron scattering mediated by critical Ising-nematic fluctuations. We argue that the critical fluctuations play a crucial role in determining the observed temperature dependence of the frequency of the quasi-elastic peak. At frequencies larger than the temperature, we find that the Raman response is proportional to $ω^{1/3}$, consistently with earlier predictions \cite{klein18a}.

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arXiv2020

Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions

Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.

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arXiv2020

Universal chiral quasi-steady states in periodically driven many-body systems

We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially filled version of Thouless's topologically quantized adiabatic pump. The corresponding single-particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless and is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window in which the system prethermalizes to an infinite-temperature state restricted to a single Floquet band. In this quasi-steady state, the time-averaged current takes a universal value determined solely by the density of particles and the topological winding number of the populated Floquet band. This remarkable behavior may be readily studied experimentally in recently developed cold atom systems.

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arXiv2020

Entropic evidence for a Pomeranchuk effect in magic angle graphene

In the 1950's, Pomeranchuk predicted that, counterintuitively, liquid 3He may solidify upon heating, due to a high excess spin entropy in the solid phase. Here, using both local and global electronic entropy and compressibility measurements, we show that an analogous effect occurs in magic angle twisted bilayer graphene. Near a filling of one electron per moir'e unit cell, we observe a dramatic increase in the electronic entropy to about 1kB per unit cell. This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature, and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly-free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons, such as the absence of a thermodynamic gap, metallicity, and a Dirac-like compressibility, and others associated with localized moments, such as a large entropy and its disappearance with magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump onsets at T~30K, the bandwidth of magnetic excitations is ~3K or smaller. The hybrid nature of the new correlated state and the large separation of energy scales have key implications for the physics of correlated states in twisted bilayer graphene.

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