arXiv subjects

Sriram Ganeshan

Publications and source records attributed to Sriram Ganeshan.

51 records · Page 3Linked to original sources

arXiv2016

Exactly soluble model of boundary degeneracy

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

cond-mat.str-el↗

arXiv2016

Measurement of topological invariants in a 2D photonic system

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk-boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number. Here, for the first time, we measure the winding number in a 2D photonic system. By inserting a unit flux quantum at the edge, we show that the edge spectrum resonances shift by the winding number. This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.

cond-mat.mes-hall↗

arXiv2016

Formalism for the solution of quadratic Hamiltonians with large cosine terms

We consider quantum Hamiltonians of the form $H = H_0 - U \sum_j \cos(C_j)$ where $H_0$ is a quadratic function of position and momentum variables $\{x_1, p_1, x_2, p_2,...\}$ and the $C_j$'s are linear in these variables. We allow $H_0$ and $C_j$ to be completely general with only two restrictions: we require that (1) the $C_j$'s are linearly independent and (2) $[C_j, C_k]$ is an integer multiple of $2πi$ for all $j,k$ so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low energy spectrum in the limit $U \rightarrow \infty$. This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite $U$ limit, we also discuss how to analyze these systems when $U$ is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

cond-mat.str-el↗

arXiv2015

Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge

We investigate many body localization in the presence of a single particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single particle mobility edge in the noninteracting system leads to a many body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the non-thermal to thermal transition. Consequently, there exists an extended non-ergodic phase for an intermediate energy window where the many body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many body localization transition despite the existence of a single particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.

cond-mat.str-el↗

arXiv2015

Parafermionic zero modes in ultracold bosonic systems

Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes.

cond-mat.quant-gas↗

arXiv2015

Nearest neighbor tight binding models with an exact mobility edge in one dimension

We investigate localization properties in a family of deterministic (i.e. no disorder) nearest neighbor tight binding models with quasiperiodic onsite modulation. We prove that this family is self-dual under a generalized duality transformation. The self-dual condition for this general model turns out to be a simple closed form function of the model parameters and energy. We introduce the typical density of states as an order parameter for localization in quasiperiodic systems. By direct calculations of the inverse participation ratio and the typical density of states we numerically verify that this self-dual line indeed defines a mobility edge in energy separating localized and extended states. Our model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry. We propose a realistic experimental scheme to realize our results in atomic optical lattices and photonic waveguides.

cond-mat.dis-nn↗

arXiv2015

Constructing a Weyl semimetal by stacking one dimensional topological phases

Topological semimetals in three-dimensions (e.g. Weyl semimetal) can be built by stacking two dimensional topological phases. The interesting aspect of such a construction is that even though the topological building blocks in the low dimension may be gapped, the higher dimensional semimetallic phase emerges as a gapless critical point of a topological phase transition between two distinct insulating phases. In this work, we extend this idea by constructing three-dimensional topological semimetallic phases akin to Weyl systems by stacking one-dimensional Aubry-Andre-Harper (AAH) lattice tight binding models with non-trivial topology. The generalized AAH model is a family of one dimensional tight binding models with cosine modulations in both hopping and onsite energy terms. In this paper, we present a two-parameter generalization of the AAH model that can access topological phases in three dimensions within a unified framework. We show that the $π$-flux state of this two-parameter AAH model manifests three dimensional topological semimetallic phases where the topological features are embedded in one dimension. The topological nature of the band touching points of the semimetallic phase in 3D is explicitly established both analytically and numerically from the 1D perspective. This dimensional reduction provides a simple protocol to experimentally construct the three dimensional Brillouin zone of the topological semimetallic phases using `legos' of simple 1D double well optical lattices. We also propose Zak phase imaging of optical lattices as a tool to capture the topological nature of the band touching points. Our work provides a theoretical connection between the commensurate AAH model in 1D and Weyl semimetals in 3D, and points toward practical methods for the laboratory realization of such three dimensional topological systems in atomic optical lattices.

cond-mat.mes-hall↗

arXiv2014

Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point

One dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two dimensional Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, no such connection has been made for the Maryland model (MM). In this work, we describe a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the 1D MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.

cond-mat.mes-hall↗

arXiv2013

Exact Classification of Landau-Majorana-Stückelberg-Zener Resonances By Floquet Determinants

Recent experiments have shown that Landau-Majorana-Stuckelberg-Zener (LMSZ) interferometry is a powerful tool for demonstrating and exploiting quantum coherence not only in atomic systems but also in a variety of solid state quantum systems such as spins in quantum dots, superconducting qubits, and nitrogen vacancy centers in diamond. In this work, we propose and develop a general (and, in principle, exact) theoretical formalism to identify and characterize the interference resonances that are the hallmark of LMSZ interferometry. Unlike earlier approaches, our scheme does not require any approximations, allowing us to uncover important and previously unknown features of the resonance structure. We also discuss the experimental observability of our results.

cond-mat.mes-hall↗

arXiv2013

Simulation of quantum zero-point effects in water using a frequency-dependent thermostat

Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point temperature, which translates into an underestimation of covalent interatomic distances due to anharmonic effects. Zero-point effects can be recovered using path integral molecular dynamics simulations, but these are computationally expensive, making their combination with ab initio molecular dynamics simulations a challenge. As an alternative to path integral methods, from a computationally simple perspective, one would envision the design of a thermostat capable of equilibrating and maintaining the different vibrational modes at their corresponding zero-point temperatures. Recently, Ceriotti et al. (Phys. Rev. Lett. 102 020601 (2009)) introduced a framework to use a custom-tailored Langevin equation with correlated noise that can be used to include quantum fluctuations in classical molecular dynamics simulations. Here we show that it is possible to use the generalized Langevin equation with suppressed noise in combination with Nose-Hoover thermostats to efficiently impose a zero-point temperature on independent modes in liquid water. Using our simple and inexpensive method, we achieve excellent agreement for all atomic pair correlation functions compared to the path integral molecular dynamics simulation.

cond-mat.stat-mech↗

arXiv2013

Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

The Aubry-André or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss the feasibility of experimental observability of our predicted topological phase in the commensurate AAH model.

cond-mat.mes-hall↗

arXiv2012

FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

We consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett models for the multiple tunneling contacts connected by the chiral single-mode FQHE edges. It is shown that the compactness of the Wen- Fröhlich chiral boson fields describing the FQHE edge modes plays a crucial role in eliminating the spurious non-locality of the electron transport properties of the FQHE interferometers arising in the regime of strong tunneling.

cond-mat.str-el↗

arXiv2011

Fluctuation Relations for Current Components in Mesoscopic Electric Circuits

We present a new class of fluctuation relations, to which we will refer as Fluctuation Relations for Current Components (FRCCs). FRCCs can be used to estimate system parameters when complete information about nonequilibrium many-body electron interactions is unavailable. We show that FRCCs are often robust in the sense that they do not depend on some basic types of electron interactions and some quantum coherence effects.

cond-mat.mes-hall↗

arXiv2011

Quasiparticle scattering from vortices in d-wave superconductors I: Superflow contribution

In the vortex state of a d-wave superconductor, massless Dirac quasiparticles are scattered from magnetic vortices via a combination of two basic mechanisms: effective potential scattering due to the superflow swirling about the vortices and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex. In this paper, we study the superflow contribution by calculating the differential cross section for a quasiparticle scattering from the effective non-central potential of a single vortex. We solve the massless Dirac equation in polar coordinates and obtain the cross section via a partial wave analysis. We also present a more transparent Born-limit calculation and in this approximation we provide an analytic expression for the differential cross section. The Berry phase contribution to the quasiparticle scattering is considered in a separate paper.

cond-mat.supr-con↗

arXiv2011

Quasiparticle scattering from vortices in d-wave superconductors. II. Berry phase contribution

In the mixed state of a d-wave superconductor, Bogoliubov quasiparticles are scattered from magnetic vortices via a combination of two effects: Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex, and effective potential scattering due to the superflow swirling about the vortices. In this paper, we consider the Berry phase contribution in the absence of superflow, which results in branch cuts between neighboring vortices across which the quasiparticle wave function changes sign. Here, the simplest problem that captures the physics is that of scattering from a single finite branch cut that stretches between two vortices. Elliptical coordinates are natural for this two-center problem, and we proceed by separating the massless Dirac equation in elliptical coordinates. The separated equations take the form of the Whittaker-Hill equations, which we solve to obtain radial and angular eigenfunctions. With these eigenfunctions in hand, we construct the scattering cross section via partial wave analysis. We discuss the scattering effect of Berry phase in the absence of superflow, having considered the superflow effect in the absence of Berry phase in a separate paper. We also provide qualitative comparison of transport cross sections for the Berry phase and the Superflow effects. The important issue of interference between the two effects is left to future work.

cond-mat.supr-con↗