arXiv subjects

A. G. Abanov

Publications and source records attributed to A. G. Abanov.

At least 19 recordsLinked to original sources

arXiv2022

Limit shape phase transitions: a merger of arctic circles

We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions - arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross-Witten-Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universal transition as the Merger Transition.

cond-mat.stat-mech↗

arXiv2022

Chiral Anomaly in Euler Fluid and Beltrami Flow

We show that the chiral anomaly of quantum field theories with Dirac fermions subject to an axial background field is an inherent property of kinematics of a perfect classical fluid. Celebrated Beltrami flows (stationary solutions of Euler equations with extensive helicity) exhibit the chiral anomaly equivalent to that known for Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current at equilibrium. We show that it is also a property of Beltrami flows.

hep-th↗

arXiv2021

Axial-Current Anomaly in Euler Fluid

We argue that a close analog of the axial-current anomaly of quantum field theories with fermions occurs in the classical Euler fluid. The conservation of the axial current (closely related to the helicity of inviscid barotropic flow) is anomalously broken by the external electromagnetic field as $\partial_μj_{A}^μ= 2\,\bf E\!\cdot\! \bf B$ similar to that of the axial current of a quantum field theory with Dirac fermions such as QED.

hep-th↗

arXiv2010

Cold Fermi-gas with long range interaction in a harmonic trap

We study equilibrium density and spin density profiles for a model of cold one-dimensional spin 1/2 fermions interacting via inverse square interaction and exchange in an external harmonic trap. This model is the well-known spin-Calogero model (sCM) and its fully nonlinear collective field theory description is known. We extend the field theory description to the presence of an external harmonic trap and obtain analytic results for statics and dynamics of the system. For instance, we find how the equilibrium density profile changes upon tuning the interaction strength. The results we obtain for equilibrium configurations are very similar to the ones obtained recently by Ma and Yang [1] for a model of fermions with short ranged interactions. Our main approximation is the neglect of the terms of higher order in spatial derivatives in equations of motion - gradientless approximation [2]. Within this approximation the hydrodynamic equations of motion can be written as a set of decoupled forced Riemann-Hopf equations for the dressed Fermi momenta of the model. This enables us to write analytical solutions for the dynamics of spin and charge. We describe the time evolution of the charge density when an initial non-equilibrium profile is created by cooling the gas with an additional potential in place and then suddenly removing the potential. We present our results as a simple "single-particle" evolution in the phase-space reminiscing a similar description of the dynamics of non-interacting one-dimensional fermions.

cond-mat.quant-gas↗

arXiv2009

Nonlinear dynamics of spin and charge in spin-Calogero model

The fully nonlinear dynamics of spin and charge in spin-Calogero model is studied. The latter is an integrable one-dimensional model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. Classical hydrodynamic equations of motion are written for this model in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation variables separate in terms of dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi momenta. We study the dynamics of some non-equilibrium spin-charge configurations for times smaller than the time-scale of the gradient catastrophe. We find an interesting interplay between spin and charge degrees of freedom. In the limit of large coupling constant the hydrodynamics reduces to the spin hydrodynamics of the Haldane-Shastry model.

cond-mat.str-el↗

arXiv2008

Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analogue of Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the Chiral Non-linear Equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the Chiral Non-Linear Equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the Chiral Non-Linear equations.

cond-mat.str-el↗

arXiv2008

Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium and provide vital tools to study non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form.

cond-mat.mes-hall↗

arXiv2008

Allowed charge transfers between coherent conductors driven by a time-dependent scatterer

We derive constraints on the statistics of the charge transfer between two conductors in the model of arbitrary time-dependent instant scattering of non-interacting fermions at zero temperature. The constraints are formulated in terms of analytic properties of the generating function: its zeroes must lie on the negative real axis. This result generalizes existing studies for scattering by a time-independent scatterer under time-dependent bias voltage.

cond-mat.mes-hall↗

arXiv2006

Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas

A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock wave phenomenon. The non-linear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the Orthogonality Catastrophe. We study a generalization of this phenomenon to the non-equilibrium regime and show how the Orthogonality Catastrophe cures the Gradient Catastrophe, providing a dispersive regularization mechanism. We show that a wave packet overturns and collapses into modulated oscillations with the wave vector determined by the height of the initial wave. The oscillations occupy a growing region extending forward with velocity proportional to the initial height of the packet. We derive a fundamental equation for the transition rates (MKP-equation) and solve it by means of the Whitham modulation theory.

cond-mat.str-el↗

arXiv2003

Bond order from disorder in the planar pyrochlore magnet

We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.

cond-mat.str-el↗

arXiv2002

Tunneling Characteristics of an Electron-Hole Trilayer under an In-plane Magnetic Field

We have studied the tunneling properties of GaSb/AlSb/InAs/AlSb/GaSb heterostructures, in which electrons and holes accumulate in the InAs and GaSb regions respectively, under a magnetic field parallel to the interfaces. The low-temperature (T = 4.2K), zero-bias magnetoconductance has shown a behavior with field that evidences the two-dimensional character of both electrons and holes and that has allowed us to determine the hole density and the electron-hole separation. The observed field dependence of the current-voltage characteristics is explained by the relative change in parallel momentum of electrons and holes induced by the field.

cond-mat.mes-hall↗

arXiv2001

Berry phase for ferromagnet with fractional spin

We study the double exchange model on two lattice sites with one conduction electron in the limit of an infinite Hund's interaction. While this simple problem is exactly solvable, we present an approximate solution which is valid in the limit of large core spins. This solution is obtained by integrating out charge degrees of freedom. The effective action of two core spins obtained in the result of such an integration resembles the action of two fractional spins. We show that the action obtained via naive gradient expansion is inconsistent. However, a ``non-perturbative'' treatment leads to an extra term in the effective action which fixes this inconsistency. The obtained ``Berry phase term'' is geometric in nature. It arises from a geometric constraint on a target space imposed by an adiabatic approximation.

cond-mat↗

arXiv2001

Geometrical phases and quantum numbers of solitons in nonlinear sigma-models

Solitons of a nonlinear field interacting with fermions often acquire a fermionic number or an electric charge if fermions carry a charge. We show how the same mechanism (chiral anomaly) gives solitons statistical and rotational properties of fermions. These properties are encoded in a geometrical phase, i.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In the most interesting cases the geometrical phase is non-perturbative and has a form of an integer-valued theta-term.

hep-th↗

arXiv2000

Chiral non-linear sigma-models as models for topological superconductivity

We study the mechanism of topological superconductivity in a hierarchical chain of chiral non-linear sigma-models (models of current algebra) in one, two, and three spatial dimensions. The models have roots in the 1D Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a point-like topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.

hep-th↗

arXiv1999

Theta-terms in nonlinear sigma-models

We trace the origin of theta-terms in non-linear sigma-models as a nonperturbative anomaly of current algebras. The non-linear sigma-models emerge as a low energy limit of fermionic sigma-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic sigma-models in spacetime dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are theta-terms. We emphasize a relation between theta-terms and quantum numbers of solitons.

hep-th↗

arXiv1998

Tunneling in the topological mechanism of superconductivity

We compute the two-particle matrix element and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic liquid consists of the compressible charge sector and the incompressible chiral topological spin liquid. We show that ground states differing by an odd number of particles are orthogonal and insertion of two extra electrons is followed by the emission of soft modes of the transversal spin current. The orthogonality catastrophe makes the physics of superconductivity drastically different from the BCS-theory but similar to the physics of one-dimensional electronic liquids. The wave function of a pair is dressed by soft modes. As a result the two particle matrix element forms a complex d-wave representation (i.e., changes sign under $90^o$ degree rotation), although the gap in the electronic spectrum has no nodes. In contrast to the BCS-theory the tunneling amplitude has an asymmetric broad peak (much bigger than the gap) around the Fermi surface. We develop an operator algebra, that allows one to compute other correlation functions.

cond-mat.str-el↗

arXiv1998

Asymptotically exact solutions of Harper equation

We present asymptotically exact solutions of an incommensurate Harper equation---one-dimensional Schroedinger equation of one particle on a lattice in a cosine potential. The wave functions can be written as an infinite product of string polynomials. The roots of these polynomials are solutions of Bethe equations. They are classified according to the string hypothesis. The string hypothesis gives asymptotically exact values of roots and reveals the hierarchical structure of the spectrum of the Harper equation.

cond-mat↗

arXiv1997

Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz

We present numerical evidence that solutions of the Bethe Ansatz equations for a Bloch particle in an incommensurate magnetic field (Azbel-Hofstadter or AH model), consist of complexes-"strings". String solutions are well-known from integrable field theories. They become asymptotically exact in the thermodynamic limit. The string solutions for the AH model are exact in the incommensurate limit, where the flux through the unit cell is an irrational number in units of the elementary flux quantum. We introduce the notion of the integral spectral flow and conjecture a hierarchical tree for the problem. The hierarchical tree describes the topology of the singular continuous spectrum of the problem. We show that the string content of a state is determined uniquely by the rate of the spectral flow (Hall conductance) along the tree. We identify the Hall conductances with the set of Takahashi-Suzuki numbers (the set of dimensions of the irreducible representations of $U_q(sl_2)$ with definite parity). In this paper we consider the approximation of noninteracting strings. It provides the gap distribution function, the mean scaling dimension for the bandwidths and gives a very good approximation for some wave functions which even captures their multifractal properties. However, it misses the multifractal character of the spectrum.

cond-mat↗