arXiv subjects

Subroto Mukerjee

Publications and source records attributed to Subroto Mukerjee.

At least 73 records · Page 4Linked to original sources

arXiv2013

Universal power law in crossover from integrability to quantum chaos

We study models of interacting fermions in one dimension to investigate the crossover from integrability to non-integrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size $L \to \infty$ non-integrability sets in for an arbitrarily small integrability-breaking perturbation. The crossover value of the perturbation scales as a power law $\sim L^{-3}$ when the integrable system is gapless and the scaling appears to be robust to microscopic details and the precise form of the perturbation. We conjecture that the exponent in the power law is characteristic of the random matrix ensemble describing the non-integrable system. For systems with a gap, the crossover scaling appears to be faster than a power law.

cond-mat.str-el↗

arXiv2012

Phases, transitions, and boundary conditions in a model of interacting bosons

We carry out an extensive study of the phase diagrams of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases. We show that the critical exponents and central charges for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different boundary conditions lead to different phase diagrams.

cond-mat.quant-gas↗

arXiv2012

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of synthetic orbital magnetic fields, we study the "fully frustrated" Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group (DMRG) method, we show that the phase diagram of such kinetically frustrated bosons displays three phases on a two-leg ladder: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable "Chiral Mott Insulator" (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, propose and study a Jastrow variational wavefunction which captures its correlations, present DMRG results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we discuss generalizations to a staggered flux Bose-Hubbard model and a two-dimensional version of the CMI with edge currents in weakly coupled ladders.

cond-mat.supr-con↗

arXiv2012

Bose Hubbard Model in a Strong Effective Magnetic Field: Emergence of a Chiral Mott Insulator Ground State

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the "fully frustrated" Bose-Hubbard (FFBH) model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

cond-mat.quant-gas↗

arXiv2010

Theromelectricity in Graphene: Effects of a gap and magnetic fields

We calculate the thermopower of monolayer graphene in various circumstances. First we show that experiments on the thermopower of graphene can be understood quantitatively with a very simple model of screening in the semiclassical limit. We can calculate the energy dependent scattering time for this model exactly. We then consider acoustic phonon scattering which might be the operative scattering mechanism in free standing films, and predict that the thermopower will be linear in any induced gap in the system. Further, the thermopower peaks at the same value of chemical potential (tunable by gate voltage) independent of the gap. Finally, we show that in the semiclassical approximation, the thermopower in a magnetic field saturates at high field to a value which can be calculated exactly and is independent of the details of the scattering. This effect might be observable experimentally.

cond-mat.mtrl-sci↗

arXiv2010

Evidence of gate-tunable topological excitations in two-dimensional electron systems

Topological defects are ubiquitous from solid state physics to cosmology, where they drive phase transitions by proliferating as domain walls, monopoles or vortices. As quantum excitations, they often display fractional charge and anyonic statistics, making them relevant to topologically protected quantum computation, but realizing a controlled physical resource for topological excitations has been difficult. Here we report evidence of topological excitations during the localization transition in strongly interacting two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures. We find the electrical conductivity at low electron densities to follow a Berezinskii-Kosterlitz Thouless (BKT)-like order-disorder transition implying a gate-tunable proliferation of charged topological defects. At low temperatures, a weakening in the temperature dependence of conductivity was observed, and linked to the zero point fluctuations and delocalization of the defects. Our experiments also cast crucial insight on the nature of the ground state in strongly interacting 2DESs in presence of disorder.

cond-mat.mes-hall↗

arXiv2009

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and non-integrable regimes. It is known from previous work that universal power laws appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two scaling regimes of the entanglement entropy and a relaxation that is power-law rather than exponential. The final state of evolution after the quench is not well characterized by any effective temperature, and the Loschmidt echo converges algebraically to a constant for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

cond-mat.str-el↗

arXiv2009

Theory of finite-entanglement scaling at one-dimensional quantum critical points

Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than non-critical states. Standard algorithms for one-dimensional many-particle systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality: the scaling theory of finite entanglement is only superficially similar to finite-size scaling, and has a different physical origin. We find that finite-entanglement scaling is governed not by the scaling dimension of an operator but by the "central charge" of the critical point, which counts its universal degrees of freedom. An important ingredient is the recently obtained universal distribution of density-matrix eigenvalues at a critical point\cite{calabrese1}. The parameter-free theory is checked against numerical scaling at several quantum critical points.

cond-mat.str-el↗

arXiv2008

Optimal thermoelectric figure of merit of a molecular junction

We show that a molecular junction can give large values of the thermoelectric figure of merit $ZT$, and so could be used as a solid state energy conversion device that operates close to the Carnot efficiency. The mechanism is similar to the Mahan-Sofo model for bulk thermoelectrics -- the Lorenz number goes to zero violating the Wiedemann-Franz law while the thermopower remains non-zero. The molecular state through which charge is transported must be weakly coupled to the leads, and the energy level of the state must be of order $k_B T$ away from the Fermi energy of the leads. In practice, the figure of merit is limited by the phonon thermal conductance; we show that the largest possible $ZT\sim(\tilde{G}_{th}^{ph})^{-1/2}$, where $\tilde{G}_{th}^{ph}$ is the phonon thermal conductance divided by the thermal conductance quantum.

cond-mat.mes-hall↗

arXiv2008

Anomalously large measured thermoelectric power factor in Sr$_{1-x}$La$_x$TiO$_3$ thin films due to SrTiO$_3$ substrate reduction

We report the observation that thermoelectric thin-films of La-doped SrTiO3 grown on SrTiO3 substrates yield anomalously high values of thermopower to give extraordinary values of power factor at 300K. Thin-films of Sr0.98La0.02TiO3, grown via pulsed laser deposition at low temperature and low pressure (450C, 10-7Torr), do not yield similarly high values when grown on other substrates. The thin-film growth induces oxygen reduction in the SrTiO3 crystals, doping the substrate n-type. It is found that the backside resistance of the SrTiO3 substrates is as low (~12ohm/square) as it is on the film-side after film growth.

cond-mat.mtrl-sci↗

arXiv2007

Vortex lattice transitions in cyclic spinor condensates

We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor Bose condensates. In addition to the familiar triangular lattice predicted by Tkachenko for $^4$He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aperiodic vortex structure.

cond-mat.other↗

arXiv2007

Dynamical thermal response functions for strongly correlated one-dimensional systems

In this article we study the thermal response functions for two one-dimensional models, namely the Hubbard and spin-less fermion $t$-$V$ models. By exactly diagonalizing finite sized systems we calculate dynamical electrical, thermoelectrical, and thermal conductivities via the Kubo formalism. The thermopower (Seebeck coefficient), Lorenz number, and dimensionless figure of merit are then constructed which are quantities of great interest to the physics community both theoretically and experimentally. We also geometrically frustrate these systems and destroy integrability by the inclusion of a second neighbor hop. These frustrated systems are shown to have enhanced thermopower and Lorenz number at intermediate and low temperatures.

cond-mat.str-el↗

arXiv2007

Signatures of integrability in charge and thermal transport in 1D quantum systems

Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the finite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $σ(q,ω)$ and $κ(q,ω)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.

cond-mat.str-el↗

arXiv2007

Dynamical models and the phase ordering kinetics of the s=1 spinor condensate

The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two dimensions in an optical trap. We study the general ground state phase diagram of a spin-1 system and focus on a phase that has a magnetic Ising order parameter and numerically determine the nature of the finite temperature superfluid and magnetic phase transitions. We then study three different dynamical models: model A, which has no conserved quantities, model F, which has a conserved second sound mode and the Gross-Pitaevskii (GP) equation which has a conserved density and magnetization. We find the dynamic critical exponent to be the same for models A and F ($z=2$) but different for GP ($z \approx 3$). Externally imposed magnetization conservation in models A and F yields the value $z \approx 3$, which demonstrates that the only conserved density relevant to domain formation is the magnetization density.

cond-mat.stat-mech↗

arXiv2006

Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions

The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We analyze the topological defects of the polar condensate, correcting previous studies, and show that the polar condensate in two dimensions is unstable at any finite temperature; instead there is a nematic or paired superfluid phase with algebraic order in $\exp(2 i θ)$, where $θ$ is the superfluid phase, and no magnetic order. The Kosterlitz-Thouless transition out of this phase is driven by unbinding of half-vortices (the spin-disordered version of the combined spin and phase defects found by Zhou), and the anomalous universal $8 T_c / π$ stiffness jump at the transition is confirmed in numerical simulations. The anomalous stiffness jump is a clear experimental signature of this phase and the corresponding phase transition.

cond-mat.other↗

arXiv2006

Doping dependence of thermopower and thermoelectricity in strongly correlated systems

The search for semiconductors with high thermoelectric figure of merit has been greatly aided by theoretical modeling of electron and phonon transport, both in bulk materials and in nanocomposites. Recent experiments have studied thermoelectric transport in ``strongly correlated'' materials derived by doping Mott insulators, whose insulating behavior without doping results from electron-electron repulsion, rather than from band structure as in semiconductors. Here a unified theory of electrical and thermal transport in the atomic and ``Heikes'' limit is applied to understand recent transport experiments on sodium cobaltate and other doped Mott insulators at room temperature and above. For optimal electron filling, a broad class of narrow-bandwidth correlated materials are shown to have power factors (the electronic portion of the thermoelectric figure of merit) as high at and above room temperature as in the best semiconductors.

cond-mat.str-el↗

arXiv2005

Towards a statistical theory of transport by strongly-interacting lattice fermions

We present a study of electric transport at high temperature in a model of strongly interacting spinless fermions without disorder. We use exact diagonalization to study the statistics of the energy eigenvalues, eigenstates, and the matrix elements of the current. These suggest that our nonrandom Hamiltonian behaves like a member of a certain ensemble of Gaussian random matrices. We calculate the conductivity $σ(ω)$ and examine its behavior, both in finite size samples and as extrapolated to the thermodynamic limit. We find that $σ(ω)$ has a prominent non-divergent singularity at $ω=0$ reflecting a power-law long-time tail in the current autocorrelation function that arises from nonlinear couplings between the long-wavelength diffusive modes of the energy and particle number.

cond-mat.str-el↗

arXiv2005

Thermopower of the Hubbard model: Effects of multiple orbitals and magnetic fields in the atomic limit

We consider strongly-correlated systems described by the multi-orbital Hubbard model in the atomic limit and obtain exact expressions for the chemical potential and thermopower. We show that these expressions reduce to the Heikes formula in the appropriate limits ($k_BT \gg U$) and ($k_BT \ll U$) and obtain the full temperature dependence in between these regimes. We also investigate the effect of a magnetic field introduced through a Zeeman term and observe that the thermopower of the multi-orbital Hubbard model displays spikes as a function of magnetic field at certain special values of the field. This effect might be observable in experiments for materials with a large magnetic coupling.

cond-mat.str-el↗