arXiv subjects

William Witczak-Krempa

Publications and source records attributed to William Witczak-Krempa.

At least 55 records · Page 3Linked to original sources

arXiv2020

Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching

Due to strong spin-orbit coupling, charge carriers in three-dimensional quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a reduced plasma frequency and an increased spectral weight at small wavevectors, compared to a regular quadratic band. This weakens the effective Coulomb potential, modifying the single-particle self-energy for which we present both analytical and numerical results. At a low carrier density, the quasiparticle properties of this model strongly deviate from that of a single quadratic band. We compare our findings with experimental results for alpha-Sn, HgSe, HgTe, YPtBi and Pr2Ir2O7.

cond-mat.mes-hall↗

arXiv2019

Geometric entanglement in integer quantum Hall states with boundaries

Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the groundstate of integer quantum Hall systems in the presence of boundaries through the reduced density matrix of a spatial region. We work in the lowest Landau level and choose our region to intersect the boundary at arbitrary angles. The entanglement entropy (EE) contains a logarithmic contribution coming from the chiral edge modes, and matches the corresponding conformal field theory prediction. We uncover an additional contribution due to the boundary corners. We characterize the angle-dependence of this boundary corner term, and compare it to the bulk corner EE. We further analyze the spatial structure of entanglement via the eigenstates associated with the reduced density matrix, and construct a spatially-resolved EE. The influence of the physical boundary and the region's geometry on the reduced density matrix is thus clarified. Finally, we discuss the implications of our findings for other topological phases, as well as quantum critical systems such as conformal field theories in 2 spatial dimensions.

cond-mat.str-el↗

arXiv2019

Monopole operators and their symmetries in QED3-Gross-Neveu models

Monopole operators are topological disorder operators in 2+1 dimensional compact gauge field theories appearing notably in quantum magnets with fractionalized excitations. For example, their proliferation in a spin-1/2 kagome Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin liquid phase to an antiferromagnet. The quantum critical point (QCP) for this transition is described by a conformal field theory: Compact quantum electrodynamics (QED3) with a fermionic self-interaction, a type of QED3-Gross-Neveu model. We obtain the scaling dimensions of monopole operators at the QCP using a state-operator correspondence and a large-N expansion, where 2N is the number of fermion flavors. We characterize the hierarchy of monopole operators at this SU(2) x SU(N) symmetric QCP.

cond-mat.str-el↗

arXiv2019

Interplay of Coulomb repulsion and spin-orbit coupling in superconducting 3D quadratic band touching Luttinger semimetals

We investigate the superconductivity of 3D Luttinger semimetals, such as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various pairing mechanisms have already been considered for these semimetals, such as from polar phonons modes, and in this work we explore pairing from the screened electron-electron Coulomb repulsion. In these materials, the small Fermi energy and the spin-orbit coupling strongly influence how charge fluctuations can mediate pairing. We find the superconducting critical temperature as a function of doping for an s-wave order parameter, and determine its sensitivity to changes in the dielectric permittivity. Also, we discuss how order parameters other than s-wave may lead to a larger critical temperature, due to spin-orbit coupling.

cond-mat.supr-con↗

arXiv2019

Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lifted and yields a non-trivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of QED3 using a large $N_f$ expansion where $2N_f$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39N_f$ at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic CP$^1$ theory. Finally, we discuss the implications of our results for quantum magnets on the Kagome lattice.

cond-mat.str-el↗

arXiv2019

Generalizing the entanglement entropy of singular regions in conformal field theories

We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for $(3+1)$-dimensional free conformal field theories (CFTs), entangling regions emanating from vertices give rise to a universal contribution $S_n^{\rm univ}= -\frac{1}{8π}f_b(n) \int_γ k^2 \log^2(R/δ)$, where $γ$ is the curve formed by the intersection of the entangling surface with a unit sphere centered at the vertex, and $k$ the trace of its extrinsic curvature. While for circular and elliptic cones this term reproduces the general-CFT result, it vanishes for polyhedral corners. For those, we argue that the universal contribution, which is logarithmic, is not controlled by a local integral, but rather it depends on details of the CFT in a complicated way. We also study the angle dependence for the entanglement entropy of wedge singularities in 3+1 dimensions. This is done for general CFTs in the smooth limit, and using free and holographic CFTs at generic angles. In the latter case, we show that the wedge contribution is not proportional to the entanglement entropy of a corner region in the $(2+1)$-dimensional holographic CFT. Finally, we show that the mutual information of two regions that touch at a point is not necessarily divergent, as long as the contact is through a sufficiently sharp corner. Similarly, we provide examples of singular entangling regions which do not modify the structure of divergences of the entanglement entropy compared with smooth surfaces.

hep-th↗

arXiv2018

Entanglement susceptibilities and universal geometric entanglement entropy

The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement entropy changes with small deformations of the entangling surface. This leads to the notion of entanglement susceptibilities. These relate the variation of the EE to the geometric variation of the subregion. We determine the form of the leading entanglement susceptibilities for a large class of scale invariant states, such as groundstates of conformal field theories, and systems with Lifshitz scaling, which includes fixed points governed by disorder. We then use the susceptibilities to derive the universal contributions that arise due to non-smooth features in the entangling surface: corners in 2d, as well as cones and trihedral vertices in 3d. We finally discuss the generalization to Renyi entropies.

cond-mat.str-el↗

arXiv2018

Entanglement signatures of emergent Dirac fermions: kagome spin liquid & quantum criticality

Quantum spin liquids (QSL) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its non-locality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density-matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL, and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge ordered phase.

cond-mat.str-el↗

arXiv2017

Quantum spin chains with multiple dynamics

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitations have a dynamical exponent $z$ that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent $2\leq z <2.7$, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wavefunction for the groundstate, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the non-equilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.

cond-mat.str-el↗

arXiv2017

Gapless quantum spin chains: multiple dynamics and conformal wavefunctions

We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for the calculation of spin and entanglement properties in a unified fashion. Doing so, we uncover an emergent conformal-type symmetry, thus consolidating the connection to a widely studied family of Lifshitz quantum critical points in 2d. We then obtain the low lying excited states via large-scale DMRG simulations and find that the dynamical exponent is z = 3.2 in both cases. Other excited states show a different z, indicating that these models have multiple dynamics. Moreover, we modify the spin-1/2 model by adding a ferromagnetic Heisenberg term, which changes the entire spectrum. We track the resulting non-trivial evolution of the dynamical exponents using DMRG. Finally, we exploit an exact map from the quantum Hamiltonian to the non-equilibrium dynamics of a classical spin chain to shed light on the quantum dynamics.

cond-mat.str-el↗

arXiv2017

Quantum critical response: from conformal perturbation theory to holography

We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high frequencies. Knowledge of the high frequency response allows us then to derive non-perturbative sum rules. We show, via explicit computations, how holography recovers the general results of CFT, and the associated sum rules, for any holographic field theory with a conformal UV completion -- regardless of any possible new ordering and/or scaling physics in the IR. We numerically obtain holographic response functions at all frequencies, allowing us to probe the breakdown of the asymptotic high-frequency regime. Finally, we show that high frequency response functions in holographic Lifshitz theories are quite similar to their conformal counterparts, even though they are not strongly constrained by symmetry.

hep-th↗

arXiv2017

Two-cylinder entanglement entropy under a twist

We study the von Neumann and Rényi entanglement entropy (EE) of scale-invariant theories defined on tori in 2+1 and 3+1 spacetime dimensions. We focus on spatial bi-partitions of the torus into two cylinders, and allow for twisted boundary conditions along the non-contractible cycles. Various analytical and numerical results are obtained for the universal EE of the relativistic boson and Dirac fermion conformal field theories (CFTs), and for the fermionic quadratic band touching and the boson with $z=2$ Lifshitz scaling. The shape dependence of the EE clearly distinguishes these theories, although intriguing similarities are found in certain limits. We also study the evolution of the EE when a mass is introduced to detune the system from its scale-invariant point, by employing a renormalized EE that goes beyond a naive subtraction of the area law. In certain cases we find non-monotonic behavior of the torus EE under RG flow, which distinguishes it from the EE of a disk.

cond-mat.str-el↗

arXiv2017

Dynamical response near quantum critical points

We study high frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from conformal field theory allow us to fix the high frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality, and numerically via Quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high frequency optical conductivity, and the corresponding sum rule.

cond-mat.str-el↗

arXiv2017

Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the $N$-linear result of the Gaussian fixed point.

cond-mat.str-el↗

arXiv2016

Holographic torus entanglement and its RG flow

We study the universal contributions to the entanglement entropy (EE) of 2+1d and 3+1d holographic conformal field theories (CFTs) on topologically non-trivial manifolds, focusing on tori. The holographic bulk corresponds to AdS-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2+1d, in the simple limit where the torus becomes a thin 1d ring, the EE reduces to a shape-independent constant $2γ$. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the RG flow of $γ$ by defining a renormalized EE that 1) is applicable to general QFTs, 2) resolves the failure of the area law subtraction, and 3) is inspired by the F-theorem. We find that the renormalized $γ$ decreases monotonically when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of non-uniqueness of such renormalized EEs both in 2+1d and 3+1d.

hep-th↗

arXiv2016

Cornering gapless quantum states via their torus entanglement

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $χ$. Focusing on scale invariant systems, we derive general non-perturbative properties for the shape dependence of $χ$, and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for $χ$ in 2d/3d within a model that arises in the study of conformal field theories (CFTs), and use them to obtain ansatzes without fitting parameters for the 2d/3d free boson CFTs. Our numerical lattice calculations show that the ansatzes are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g. Kitaev's honeycomb model.

cond-mat.str-el↗

arXiv2016

Optical conductivity of topological surface states with emergent supersymmetry

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample's surface. Here, we obtain exact results for the zero- and finite-temperature optical conductivity at the semimetal-superconductor QCP for these topological surface states. This strongly interacting QCP is described by a scale invariant theory with emergent supersymmetry, which is a unique symmetry mixing bosons and fermions. We show that supersymmetry implies exact relations between the optical conductivity and two otherwise unrelated properties: the shear viscosity and the entanglement entropy. We discuss experimental considerations for the observation of these signatures in TIs.

cond-mat.str-el↗

arXiv2016

Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions when the partition involves a corner of angle $θ$, the subleading term is logarithmic with coefficient $a_α(θ)$ for the $α$-Rényi entropy. In the smooth limit $θ\!\to\!π$, $a_1(θ)$ yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general Rényi indices and angles, $a_α(θ)$ is richer and few general results exist. We study $a_α(θ)$ focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in $θ,α$ regimes hitherto unexplored. We derive field theory estimates for $a_α(θ)$, including new exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of $a_α(θ)$ for various theories, including interacting $O(N)$ models.

cond-mat.str-el↗