arXiv subjects

Andrew M. Essin

Publications and source records attributed to Andrew M. Essin.

12 recordsLinked to original sources

arXiv2014

Spectroscopic signatures of crystal momentum fractionalization

We consider gapped Z2 spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry enriched topological phases. Considering square lattice space group and time reversal symmetry, we show that exactly four distinct types of spectral periodicity are possible.

cond-mat.str-el↗

arXiv2013

Z2 topological invariants in two dimensions from quantum Monte Carlo

We employ quantum Monte Carlo techniques to calculate the $Z_2$ topological invariant in a two-dimensional model of interacting electrons that exhibits a quantum spin Hall topological insulator phase. In particular, we consider the parity invariant for inversion-symmetric systems, which can be obtained from the bulk's imaginary-time Green's function after an appropriate continuation to zero frequency. This topological invariant is used here in order to study the trivial-band to topological-insulator transitions in an interacting system with spin-orbit coupling and an explicit bond dimerization. We discuss the accessibility and behavior of this topological invariant within quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2013

Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions

We classify distinct types of quantum number fractionalization occurring in two-dimensional topologically ordered phases, focusing in particular on phases with Z2 topological order, that is, on gapped Z2 spin liquids. We find that the fractionalization class of each anyon is an equivalence class of projective representations of the symmetry group, corresponding to elements of the cohomology group H^2(G,Z2). This result leads us to a symmetry classification of gapped Z2 spin liquids, such that two phases in different symmetry classes cannot be connected without breaking symmetry or crossing a phase transition. Symmetry classes are defined by specifying a fractionalization class for each type of anyon. The fusion rules of anyons play a crucial role in determining the symmetry classes. For translation and internal symmetry, braiding statistics plays no role, but can affect the classification when point group symmetries are present. For square lattice space group, time reversal and SO(3) spin rotation symmetry, we find 2,098,176 ~ 2^21 distinct symmetry classes. We give an explicit construction of symmetry classes for square lattice space group symmetry in the toric code model. Via simple examples, we illustrate how information about fractionalization classes can in principle be obtained from the spectrum and quantum numbers of excited states. Moreover, the symmetry class can be partially determined from the quantum numbers of the four degenerate ground states on the torus. We also extend our results to arbitrary Abelian topological orders, and compare our classification with the related projective symmetry group classification of parton mean-field theories. Our results provide a framework for understanding and probing the sharp distinctions among symmetric Z2 spin liquids, and are a first step toward a full classification of symmetric topologically ordered phases.

cond-mat.str-el↗

arXiv2013

Topological invariants for the fractional quantum Hall states

We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.

cond-mat.str-el↗

arXiv2012

Topological invariants and interacting one-dimensional fermionic systems

We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the existence of topologically protected, zero-energy states at the boundaries of these systems can be tied to the values of their topological invariant, just like when working with the conventional, noninteracting topological insulators. We use a combination of analytical methods and the numerical density matrix renormalization group method to calculate the values of the topological invariant throughout the phase diagrams of these systems, thus deducing when topologically protected boundary states are present. We are also able to study topological states in spin systems because, deep in the Mott insulating regime, these fermionic systems reduce to spin chains. In this way, we associate the zero-energy states at the end of an antiferromagnetic spin-one Heisenberg chain with the topological invariant 2.

cond-mat.str-el↗

arXiv2012

Antiferromagnetic topological insulators in cold atomic gases

We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of this potential. We discuss the physically observable responses of the gas that can verify the presence of this phase. We also point out how this model can be used to obtain two-dimensional flat bands with nonzero Chern number.

cond-mat.quant-gas↗

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↗

arXiv2010

Antiferromagnetic topological insulators

We consider antiferromagnets breaking both time-reversal (Theta) and a primitive lattice translational symmetry (T) of a crystal but preserving the combination S = Theta T. The S symmetry leads to a Z_2 topological classification of insulators, separating the ordinary insulator phase from the "antiferromagnetic topological insulator" (AFTI) phase. This state is similar to the "strong" topological insulator with time-reversal symmetry, and shares with it such properties as a quantized magnetoelectric effect. However, for certain surfaces the surface states are intrinsically gapped with a half-quantum Hall effect (sigma_{xy} = e^2 / 2h), which may aid experimental confirmation of theta = pi quantized magnetoelectric coupling. Step edges on such a surface support gapless, chiral quantum wires. In closing we discuss GdBiPt as a possible example of this topological class.

cond-mat.mes-hall↗

arXiv2010

Orbital magnetoelectric coupling in band insulators

Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously shown to be quantized in topological insulators. In general materials there are additional orbital contributions to all parts of the magnetoelectric tensor; these vanish in topological insulators by symmetry and also vanish in several simplified models without time-reversal and inversion those magnetoelectric couplings were studied before. We give two derivations of the response formula, one based on a uniform magnetic field and one based on extrapolation of a long-wavelength magnetic field, and discuss some of the consequences of this formula.

cond-mat.mes-hall↗

arXiv2010

Magnetic phase diagram of a spin-1 condensate in two dimensions with dipole interaction

Several new features arise in the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. This modulation should be observable for current experimental parameters in $^{87}$Rb. Hence the much-sought supersolid state, with broken continuous translation invariance in one direction and broken global U(1) invariance, occurs generically as a metastable state in this system as a result of dipole interaction. The ferromagnetic state parallel to the applied magnetic field becomes striped in a finite system at strong dipolar coupling.

cond-mat.quant-gas↗

arXiv2009

Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wavefunction and defines the 3D topological insulator, like the IQHE, in terms of a topological ground-state response function.

cond-mat.mes-hall↗

arXiv2007

Topological insulators beyond the Brillouin zone via Chern parity

The topological insulator is an electronic phase stabilized by spin-orbit coupling that supports propagating edge states and is not adiabatically connected to the ordinary insulator. In several ways it is a spin-orbit-induced analogue in time-reversal-invariant systems of the integer quantum Hall effect (IQHE). This paper studies the topological insulator phase in disordered two-dimensional systems, using a model graphene Hamiltonian introduced by Kane and Mele as an example. The nonperturbative definition of a topological insulator given here is distinct from previous efforts in that it involves boundary phase twists that couple only to charge, does not refer to edge states, and can be measured by pumping cycles of ordinary charge. In this definition, the phase of a Slater determinant of electronic states is determined by a Chern parity analogous to Chern number in the IQHE case. Numerically we find, in agreement with recent network model studies, that the direct transition between ordinary and topological insulators that occurs in band structures is a consequence of the perfect crystalline lattice. Generically these two phases are separated by a metallic phase, which is allowed in two dimensions when spin-orbit coupling is present. The same approach can be used to study three-dimensional topological insulators.

cond-mat.mes-hall↗