arXiv subjects

Victor Gurarie

Publications and source records attributed to Victor Gurarie.

48 records · Page 3Linked to original sources

arXiv2011

Bulk-boundary correspondence of topological insulators from their Green's functions

Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's functions. Here we show that the existence of the edge states directly follows from the existence of the topological invariant written in terms of the Green's functions, for all ten classes of topological insulators in all spatial dimensions. We also show that the resulting edge states are characterized by their own topological invariant, whose value is equal to the topological invariant of the bulk insulator. This can be used to test whether a given model Hamiltonian can describe an edge of a topological insulator. Finally, we observe that the results discussed here apply equally well to interacting topological insulators, with certain modifications.

cond-mat.mes-hall↗

arXiv2011

Lattice Induced Resonances in One Dimensional Bosonic Systems

We study the resonant effects produced when a Feshbach dimer crosses a scattering continuum band of atoms in an optical lattice. We numerically obtain the exact spectrum of two particles in a one-dimensional lattice and develop an effective atom-dimer Hamiltonian that accurately captures resonant effects. The lattice-induced resonances lead to the formation of bound states simultaneously above and below the scattering continuum and significantly modify the curvature of the dimer dispersion relation. The nature of the atom-dimer coupling depends strongly on the parity of the dimer state leading to a novel coupling in the case of negative parity dimers. From the exact solutions we extract the dimer Wannier function from which we quantitatively determine the effective Hamiltonian parameters for a many-body description.

cond-mat.quant-gas↗

arXiv2011

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wavefunctions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wavefunctions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.

cond-mat.str-el↗

arXiv2010

High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices

We calculate experimentally relevant properties of trapped fermionic alkaline earth atoms in an optical lattice, modeled by the SU(N) Hubbard model. Our calculation is accurate when the temperature is much larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a non-interacting gas, as a function of initial gas temperature and final state lattice parameters. Of particular experimental interest, we find that increasing $N$ gives substantially \textit{colder} Mott insulators, up to more than a factor of five for relevant parameters. This cooling happens for all $N$, fixing the initial entropy, or for all $N \lsim 20$ (the exact value depends on dimensionality), fixing the initial temperature.

cond-mat.quant-gas↗

arXiv2010

Heavy fermions in an optical lattice

We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous system this mean-field theory is believed to give a qualitatively correct description of heavy fermion metals and Kondo insulators: it reproduces the Kondo-like scaling of the quasiparticle mass in the former, and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy fermion systems survives the confinement, and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center.

cond-mat.quant-gas↗

arXiv2009

A note on a relation between ac Josephson effect and double-well BEC oscillations

In this brief note we comment on the relation between the ac Josephson effect and the coherent oscillations of a Bose-Einstein condensate confined to a double-well potential. The goal is to elucidate the extent to which the latter is a realization of the former. We detail the correspondence that emerges in the high occupation limit of the double-well potential, and particularly note the relation between the two oscillation frequencies.

cond-mat.quant-gas↗

arXiv2009

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid

We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.

cond-mat.quant-gas↗

arXiv2009

Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras

We present a general method to obtain the central charge and quasihole scaling dimension directly from groundstate and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific clustering properties. We then use our method to examine the relation between Jack symmetric functions and certain W-algebras. We add substantially to the evidence that the (k,r) admissible Jack functions correspond to correlators of the conformal field theory W_k(k+1,k+r), by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. For the Jacks described by unitary W-models, the central charge and quasihole exponents match the ones previously obtained from analyzing the physics of the edge excitations. For the Jacks described by non-unitary W-models the central charge and quasihole scaling dimensions obtained from the wavefunctions differ from the ones obtained from the edge physics, which instead agree with the "effective" central charge of the corresponding W-model.

cond-mat.mes-hall↗

arXiv2006

Superfluid transition in a rotating resonantly-interacting Fermi gas

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial harmonic trap with frequencies $Ω_\perp$, $Ω_z$. Our primary prediction is the upper-critical angular velocity, $ω_{c2} (δ,T)$, as a function of temperature $T$ and resonance detuning $δ$, ranging across the BEC-BCS crossover. The rotation-driven suppression of superfluidity at $ω_{c2}$ is quite distinct in the BCS and BEC regimes, with the former controlled by Cooper-pair depairing and the latter by the dilution of bosonic molecules. At low $T$ and $Ω_z\llΩ_\perp$, in the BCS and crossover regimes of $0 \lesssim δ\lesssim δ_c$, $ω_{c2}$ is implicitly given by $\hbar \sqrt{ω_{c2}^2 +Ω_\perp^2}\approx 2Δ\sqrt{\hbar Ω_\perp/ε_F}$, vanishing as $ω_{c2} \simΩ_\perp(1-δ/δ_c)^{1/2}$ near $δ_c\approx 2ε_{F} + \fracγ2ε_{F} \ln(ε_F/\hbarΩ_\perp)$ (with $Δ$ the BCS gap and $γ$ resonance width), and extending bulk result $\hbarω_{c2} \approx 2Δ^2/ε_{F}$ to a finite number of atoms in a trap. In the BEC regime of $δ< 0$ we find $ω_{c2} \toΩ^-_\perp$, where molecular superfluidity can only be destroyed by large quantum fluctuations associated with comparable boson and vortex densities.

cond-mat.supr-con↗

arXiv2001

Tracer diffusion in a dislocated lamellar system

Many lamellar systems exhibit strongly anisotropic diffusion. When the diffusion across the lamellae is slow, an alternative mechanism for transverse transport becomes important. A tracer particle can propagate in the direction normal to the lamellae, never leaving a particular layer, by going around a screw dislocation. Given the density of positive and negative screw dislocations, we calculate the statistical properties of the transverse transport. When either positive or negative dislocations are in excess, the tracer moves ballistically normally to the layers with the mean square of the displacement growing like the square of time T^2. When the average dislocation charge is zero, the mean square of the normal displacement grows like T log T for large times. To obtain this result, the trajectory of the tracer must be smoothed over distances of order of the dislocation core size.

cond-mat.stat-mech↗

arXiv1999

Orthogonality Catastrophe and Spontaneous Symmetry Breaking in Double-layer Fermi-liquid-like States

The double-layer electron system with total filling factor $ν=1/2$ can be regarded as two separate Fermi-liquid-like states with $ν=1/4$ when the layer separation is sufficiently large and there is no tunneling. The weak tunneling in this state suffers an orthogonality catastrophe and it becomes irrelevant. Using the symmetric and antisymmetric combinations of layer indices as the pseudospin degrees of freedom, we show that there exists the first order transition from the above pseudospin unpolarized state to the pseudospin polarized Fermi-liquid-like state with $ν=1/2$ as the tunneling strength becomes sufficiently large.

cond-mat.mes-hall↗

arXiv1997

A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States

We present an approach to the computation of the non-Abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlation functions. The non-Abelian statistics of multi-quasihole states follows from an additional assumption.

cond-mat.mes-hall↗