arXiv subjects

Sergej Moroz

Publications and source records attributed to Sergej Moroz.

At least 55 records · Page 3Linked to original sources

arXiv2017

Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors

Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. In this work, we develop a unified low-energy description for spin-singlet paired states by deriving topological Chern-Simons field theories for $s$-wave, $d+id$, and chiral higher even-wave superconductors. These theories capture the quantum statistics and fusion rules of Bogoliubov quasiparticles and vortices and incorporate global continuous symmetries - specifically, spin rotation and conservation of magnetic flux - present in all singlet superconductors. For all such systems, we compute the Hall response for these symmetries and investigate the physics at the edge. In particular, the weakly-coupled phase of a chiral $d+id$ chiral state has a spin Hall coefficient $ν_s=2$ and a vanishing Hall response for the magnetic flux symmetry. We argue that the latter is a generic result for two-dimensional superconductors with gapped photons, thereby demonstrating the absence of a spontaneous magnetic field in the ground state of chiral superconductors. It is also shown that the Chern-Simons theories of chiral spin-singlet superconductors derived here fall into Kitaev's 16-fold classification of topological superconductors.

cond-mat.supr-con↗

arXiv2016

Chiral $p\pm ip$ superfluid on a sphere

We consider a spinless fermionic $p\pm ip$ superfluid living on a two-dimensional sphere. Using superfluid hydrodynamics we show that the ground state necessarily exhibits topological defects: either a pair of elementary vortices or a domain wall between $p\pm ip$ phases. In the topologically nontrivial BCS phase we identify the chiral fermion modes localized on the topological defects and compute their low-energy spectrum.

cond-mat.quant-gas↗

arXiv2015

Generalized Efimov effect in one dimension

We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.

cond-mat.other↗

arXiv2015

Galilean invariance at quantum Hall edge

We construct the theory of a chiral Luttinger liquid that lives on the boundary of a Galilean invariant quantum Hall fluid. In contrast to previous studies, Galilean invariance of the total (bulk plus edge) theory is guaranteed. We consider electromagnetic response at the edge and calculate momentum- and frequency-dependent electric conductivity and argue that its experimental measurement can provide a new means to determine the shift and bulk Hall viscosity.

cond-mat.str-el↗

arXiv2015

Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation

We present a theory of Galilean-invariant conventional and chiral $p_x \pm ip_y$ fermionic superfluids at zero temperature in two spatial dimensions in terms of a dual gauge theory. Our formulation is general coordinate invariant. The parity-violating effects are encoded in the Wen-Zee term that gives rise to the Hall viscosity and edge current. We show that the relativistic superfluid with the Euler current reduces to the chiral superfluid in the limit $c\to\infty$. Using Newton-Cartan geometry we construct the covariant formulation of the effective theory and calculate the energy current.

cond-mat.quant-gas↗

arXiv2014

Super Efimov effect for mass-imbalanced systems

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a p-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $l=\pm1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.03404 for identical bosons and 2.41421 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

cond-mat.quant-gas↗

arXiv2014

Topological interactions of Nambu-Goldstone bosons in quantum many-body systems

We classify effective actions for Nambu-Goldstone (NG) bosons assuming absence of anomalies. Special attention is paid to Lagrangians invariant only up to a surface term, shown to be in a one-to-one correspondence with Chern-Simons (CS) theories for unbroken symmetry. Without making specific assumptions on spacetime symmetry, we give explicit expressions for these Lagrangians, generalizing the Berry and Hopf terms in ferromagnets. Globally well-defined matrix expressions are derived for symmetric coset spaces of broken symmetry. The CS Lagrangians exhibit special properties, on both the perturbative and the global topological level. The order-one CS term is responsible for non-invariance of canonical momentum density under internal symmetry, known as the linear momentum problem. The order-three CS term gives rise to a novel type of interaction among NG bosons. All the CS terms are robust against local variations of microscopic physics.

hep-th↗

arXiv2014

Effective theory of chiral two-dimensional superfluids

We construct, to leading orders in the momentum expansion, an effective theory of a chiral $p_x + ip_y$ two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This theory naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. The particle number current and stress tensor are computed and their linear response to electromagnetic and gravitational sources is calculated. We also consider an isolated vortex in a chiral superfluid and identify the leading chirality effect in the density depletion profile.

cond-mat.quant-gas↗

arXiv2014

Non-Relativistic Parity-Violating Hydrodynamics in Two Spatial Dimensions

We construct the non-relativistic parity-violating hydrodynamic description of a two-dimensional dissipative, normal fluid in presence of small U(1) background fields and vorticity. This is achieved by taking the non-relativistic limit of the recently developed relativistic hydrodynamics in 2+1 dimensions. We identify and interpret the resulting parity-violating contributions to the non-relativistic constitutive relations, which include the Hall current flowing perpendicular to the temperature gradient, the Hall viscosity and the Leduc-Righi energy current. Also a comparison of our findings is made with the non-relativistic parity-violating hydrodynamics obtained from a light-cone dimensional reduction.

cond-mat.mes-hall↗

arXiv2013

Super Efimov effect of resonantly interacting fermions in two dimensions

We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a p-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum l=\pm1 and their binding energies obey a universal doubly exponential scaling E_3^{(n)}\propto\exp(-2e^{3πn/4+θ}) at large n. This "super Efimov effect" is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are l=\pm2 four-body resonances associated with every three-body bound state at E_4^{(n)}\propto\exp(-2e^{3πn/4+θ-0.188}). These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.

cond-mat.quant-gas↗

arXiv2012

Efimov physics from the functional renormalization group

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS-BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.

cond-mat.quant-gas↗

arXiv2012

On a scale-invariant Fermi gas in a time-dependent harmonic potential

We investigate a scale-invariant two-component Fermi gas in a time-dependent isotropic harmonic potential. The exact time evolution of the density distribution in position space in any spatial dimension is obtained. Two experimentally relevant examples, an abrupt change and a periodic modulation of the trapping frequency are solved. Small deviations from scale invariance and isotropy of the confinement are addressed within first order perturbation theory. We discuss the consequences for experiments with ultracold quantum gases such as the excitation of a tower of undamped breathing modes and a new alternative for measuring the Tan contact.

cond-mat.quant-gas↗

arXiv2012

Towards a gravity dual of the unitary Fermi gas

Inspired by the method of null dimensional reduction and by the holographic correspondence between Vasiliev's higher-spin gravity and the critical O(N) model, a bulk dual of the unitary and the ideal non-relativistic Fermi gases is proposed.

hep-th↗

arXiv2012

Symmetries and currents of the ideal and unitary Fermi gases

The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed.

hep-th↗

arXiv2011

Quantum phase transition in Bose-Fermi mixtures

We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show that a repulsive boson-boson interaction is necessary for thermodynamic stability. The quantum phase diagram is mapped in chemical potential and density space, and both first and second order quantum phase transitions are found. We discuss typical characteristics of the first order transition, such as hysteresis or a droplet formation of the condensate which may be searched for experimentally.

cond-mat.quant-gas↗

arXiv2011

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O=ψψ. We analytically compute the scaling dimension of this operator and determine the propagator <0|T O O^{\dagger}|0>. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.

hep-th↗

arXiv2010

Renormalization group study of the four-body problem

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.

cond-mat.quant-gas↗

arXiv2010

Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence

We propose that there is no analogue of the Breitenlohner-Freedman stability bound on the mass of a scalar field in the context of the nonrelativistic AdS/CFT correspondence. Our treatment is based on an equivalence between the field equation of a complex scalar in the AdS/CFT correspondence and the one-dimensional Schroedinger equation with an inverse square potential. We compute the two-point boundary correlation function for m^2<m_{BF}^2 and discuss its relation to renormalization group limit cycles and the Efimov effect in quantum mechanics. The equivalence also helps to elucidate holographic renormalization group flows and calculations in the global coordinates for Schroedinger spacetime.

hep-th↗