arXiv subjects

Sauri Bhattacharyya

Publications and source records attributed to Sauri Bhattacharyya.

11 recordsLinked to original sources

arXiv2026

Dynamics of Majorana tetron qubits under quasiparticle poisoning

We study the dissipative dynamics of a Majorana tetron qubit in the presence of extrinsic quasiparticle poisoning due to the coupling to external leads. From the Bloch-Redfield equation describing a finite-size topological superconductor hosting four Majorana zero modes and tunnel-coupled to fermionic reservoirs, we recover analytical expressions for the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the decoherence rate is gradually removed by the energy splitting of the qubit states. These results can be useful to understand time-domain experimental data in Majorana qubit prototypes.

cond-mat.mes-hall↗

arXiv2026

The charge density fluctuations and the Shrinking Fermi Liquid scenario for strange metallicity in cuprates

We interpret the strange metal (SM) properties of slightly overdoped cuprates in terms of the recently proposed Shrinking Fermi Liquid theory. This is based on the pervading presence in the cuprate phase diagram of charge density fluctuations (CDF), which have been identified and characterized in RIXS. These fluctuations are abundant and have a low energy due to the proximity of the charge density wave quantum critical point hidden under the superconducting dome of cuprates, but have a short range and non-critical character with a finite energy M/\gamma ~10 meV as measured above Tc. Here M~ \xi^-2 is determined by the short correlation length \xi, while \gamma encodes the Landau damping ruling the lifetime of the charge fluctuations. Besides these low energy CDF, cuprates also display phonons and a broad continuum of particle-hole excitations, mostly due to spin paramagnons arising from their strongly correlated character. With these experimentally characterized ingredients we show that above Tc the SM properties in transport are well described in terms of fermionic Landau quasiparticles scattering with CDF and phonons. The optical properties can instead be interpreted by the combined effect of low energy CDF determining the temperature dependence, and of the paramagnon continuum determining a linear in frequency scattering rate. Remarkably, the combined effect of these simple ingredients also induces \omega/T scaling properties for frequencies larger than M/\gamma. When superconductivity is suppressed by strong magnetic fields the SM properties extend down to a few Kelvin. By assuming that the CDF dissipation parameter \gamma grows logarithmically by lowering T, we account for all anomalous transport and thermodynamic properties of cuprates (specific heat, Seebeck, heat transport, resistivity, and magnetoresistance) thereby providing a consistent scenario for the SM phase of cuprates.

cond-mat.str-el↗

arXiv2026

Decoherence of Majorana zero modes mediated by gapless fermions

We study the decoherence of a collection of Majorana zero modes weakly coupled to a gapless reservoir of non-interacting fermions. Using the Born-Markov approximation, we derive a Lindblad master equation for the dissipative dynamics of the Majorana zero modes. Due to the long-range coupling between Majorana zero modes mediated by the gapless reservoir, the Lindblad jump operators are non-local linear combinations of the Majorana operators. We show that, as a consequence, the dissipative dynamics can exhibit long relaxation times, i.e. a slow decay of fermion parities. A spectral analysis of the Liouvillian shows that the slow-down is suppressed as a power law of the distance between Majorana zero modes. Finally, we validate the Lindblad equation by comparison with unbiased numerical simulations of the time evolution of the full density matrix. In particular, these illustrate that non-Markovian dynamics establishes non-local correlations at small times.

cond-mat.mes-hall↗

arXiv2024

Quantum Transport Theory of Strongly Correlated Matter

This report reviews recent progress in computing Kubo formulas for general interacting Hamiltonians. The aim is to calculate electric and thermal magneto-conductivities in strong scattering regimes where Boltzmann equation and Hall conductivity proxies exceed their validity. Three primary approaches are explained. 1. Degeneracy-projected polarization formulas for Hall-type conductivities, which substantially reduce the number of calculated current matrix elements. These expressions generalize the Berry curvature integral formulas to imperfect lattices. 2. Continued fraction representation of dynamical longitudinal conductivities. The calculations produce a set of thermodynamic averages, which can be controllably extrapolated using their mathematical relations to low and high frequency conductivity asymptotics. 3. Hall-type coefficients summation formulas, which are constructed from thermodynamic averages. The thermodynamic formulas are derived in the operator Hilbert space formalism, which avoids the opacity and high computational cost of the Hamiltonian eigenspectrum. The coefficients can be obtained by well established imaginary-time Monte Carlo sampling, high temperature expansion, traces of operator products, and variational wavefunctions at low temperatures. We demonstrate the power of approaches 1--3 by their application to well known models of lattice electrons and bosons. The calculations clarify the far-reaching influence of strong local interactions on the metallic transport near Mott insulators. Future directions for these approaches are discussed.

cond-mat.str-el↗

arXiv2023

Metallic transport of hard core bosons

Conductivities and Hall coefficients of two dimensional hard core bosons are calculated using the thermodynamic expansions of Kubo formulas. At temperatures above the superfluid transition, the resistivity rises linearly and is weakly dependent on boson filling. The zeroth order Hall coefficient diverges toward zero and unit fillings, and reverses its sign at half filling. The correction terms, which are calculated up to fourth (Krylov) orders, do not alter this behavior. The high temperature thermal Hall coefficient is reversed relative to the electric Hall coefficient. We discuss relevance of HCB transport to the metallic state of short coherence length superconductors.

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arXiv2022

Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator

The Hall coefficient exhibits anomalous behavior in lightly doped Mott insulators. For strongly interacting electrons its computation has been challenged by analytical and numerical obstacles. We calculate the leading contributions in the recently derived thermodynamic formula for the Hall coefficient. We obtain its doping and temperature dependence for the square lattice tJ-model at high temperatures. The second order corrections are evaluated to be negligible. Quantum Monte Carlo sampling extends our results to lower temperatures. We find a divergence of the Hall coefficient toward the Mott limit and a sign reversal relative to Boltzmann equation's weak scattering prediction. The Hall current near the Mott phase is carried by a low density of spin-entangled vacancies, which should constitute the Cooper pairs in any superconducting phase at lower temperatures.

cond-mat.str-el↗

arXiv2021

Dynamics of magnetic collective modes in the square and triangular lattice Mott insulators at finite temperature

We study the equilibrium dynamics of magnetic moments in the Mott insulating phase of the Hubbard model on the square and triangular lattice. We rewrite the Hubbard interaction in terms of an auxiliary vector field and use a recently developed Langevin scheme to study its dynamics. A thermal `noise', derivable approximately from the Keldysh formalism, allows us to study the effect of finite temperature. At strong coupling, $U \gg t$, where $U$ is the local repulsion and $t$ the nearest neighbour hopping, our results reproduce the well known dynamics of the nearest neighbour Heisenberg model with exchange $J \sim {\cal O}(t^2/U)$. These include crossover from weakly damped dispersive modes at temperature $T \ll J$ to strong damping at $T \sim {\cal O}(J)$, and diffusive dynamics at $T \gg J$. The crossover temperatures are naturally proportional to $J$. To highlight the progressive deviation from Heisenberg physics as $U/t$ reduces we compute an effective exchange scale $J_{eff}(U)$ from the low temperature spin wave velocity. We discover two features in the dynamical behaviour with decreasing $U/t$: (i)~the low temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii)~the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/J_{eff}$. We relate this to enhanced mode coupling, in particular to thermal amplitude fluctuations, at weaker $U/t$. A comparison of the square and triangular lattice reveals the additional effect of geometric frustration on damping.

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arXiv2020

Thermal dynamics of lattice modes near a polaronic crossover: from the dilute polaron limit to a charge ordered state

We provide a comprehensive solution to the lattice dynamics problem in the two dimensional Holstein model at finite electron density and finite temperature. We work in the physically relevant adiabatic regime and vary the electron-phonon interaction from the weak coupling perturbative window to the strong coupling polaronic regime. We explore three typical electron densities, dilute - where spatial correlations between polarons is weak, intermediate - where correlations are significant, and half-filling - where there is long range checkerboard order at low temperature. We use two methods both of which exploit the "slowness" of the phonons to handle the problem. These are (i)~a standard random phase approximation (RPA), adapted to capture small quantum fluctuations on Monte Carlo generated classical thermal backgrounds, and (ii)~a Langevin dynamics scheme, with a simplified ``thermal noise'', that can address large amplitude dynamical fluctuations. The Langevin scheme, as we argue in the paper, is the superior method in the strong coupling part of the phase diagram, where lattice distortions are large. It reveals a non trivial multi-peak momentum resolved spectrum with a high energy part, on the scale of the bare phonon frequency $Ω$, and a low energy peak at $ω\ll Ω$. Below the polaronic threshold, the high energy dispersion changes only modestly with temperature $T$, while the broadening, arising from mode coupling, increases linearly with $T$ at low temperature. The low energy peak shows up at strong coupling and finite temperature and arises from the slow tunneling of polarons. The tunneling events become spatially correlated as electron density increases towards half-filling, and the weight becomes strongly momentum and temperature dependent. We suggest the analytic basis of these results.

cond-mat.str-el↗

arXiv2019

Strongly anharmonic collective modes in a coupled electron-phonon-spin problem

We solve for the finite temperature collective mode dynamics in the Holstein-double exchange problem, using coupled Langevin equations for the phonon and spin variables. We present results in a strongly anharmonic regime, close to a polaronic instability. For our parameter choice the system transits from an `undistorted' ferromagnetic metal at low temperature to a structurally distorted paramagnetic insulator at high temperature, through a short range charge ordered (CO) phase near the ferromagnetic crossover at $T_{FM}$. The small amplitude harmonic phonons at low temperature cross over to large amplitude dynamics around $0.5 T_{FM}$ due to thermally generated short range correlated polarons. The rare thermal ``tunneling'' of CO domains generates a hitherto unknown momentum selective spectral weight at very low energy. We compare our results to inelastic neutron data in the manganites and suggest how the singular low energy features can be probed.

cond-mat.str-el↗

arXiv2019

A Langevin approach to lattice dynamics in a charge ordered polaronic system

We use a Langevin approach to treat the finite temperature dynamics of displacement variables in the half-filled spinless Holstein model. Working in the adiabatic regime we exploit the smallness of the adiabatic parameter to simplify the memory effects and estimate displacement costs from an "instantaneous" electronic Hamiltonian. We use a phenomenological damping rate, and uncorrelated thermal noise. The low temperature state has checkerboard charge order (CO) and the Langevin scheme generates equilibrium thermodynamic properties that accurately match Monte Carlo results. It additionally yields the dynamical structure factor, $D({\bf q}, ω)$, from the displacement field $x({\bf r}, t)$. We observe four regimes with increasing temperature, $T$, classified in relation to the charge ordering temperature, $T_c$, and the `polaron formation' temperature $T_P$, with $ T_c \ll T_P$. For $T \ll T_c$ the oscillations are harmonic, leading to dispersive phonons, with increasing $T$ bringing in anharmonic, momentum dependent, corrections. For $T \sim T_c$, thermal tunneling events of the $x({\bf r})$ field occur, with a propagating `domain' pattern at wavevector ${\bf q} \sim (π, π)$ and low energy weight in $D({\bf q}, ω)$. When $T_c < T < T_P$, the disordered polaron regime, domain structures vanish, the dispersion narrows, and low energy weight is lost. For $T \gtrsim T_P$ we essentially have uncorrelated local oscillations. We propose simple models to analyse this rich dynamics.

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arXiv2018

Modeling dynamical phonon fluctuations across the magnetically driven polaron crossover in the manganites

We investigate the dynamical structure factor associated with lattice fluctuations in a model that approximates the manganites. It involves electrons strongly coupled to core spins, and to lattice distortions, in a weakly disordered background. This model is solved in the adiabatic limit in two dimensions via Monte Carlo, retaining all the thermal fluctuations. In the metallic phase near the polaronic crossover this approach captures the effect of thermally induced polaron formation, and their short range correlation, on the electronic spectral functions. The dynamical fluctuations of the optical and acoustic phonon modes are computed at a `one loop' level by calculating the electronic polarisability in the the thermally fluctuating backgrounds, and solving the phonon Dyson equations in real space. We present phonon lineshapes across the ferromagnet to paramagnet thermal transition and correlate them with changing electronic properties. We compare our results with inelastic neutron scattering data on the metallic manganites, and also predict what one may find in the more insulating phases.

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