Quantum Transport Theory of Strongly Correlated Matter
arXiv:2406.02677 · doi:10.1016/j.physrep.2024.09.005
Abstract
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.
81 pages, 32 figures, 144 references
References in corpus (74)
- The density-matrix renormalization group in the age of matrix product states
- Synthetic magnetic fields for ultracold neutral atoms
- The ITensor Software Library for Tensor Network Calculations
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Anomalous Hall effect in ferromagnetic semiconductors
- Graphene Bilayers with a Twist
- Quantum Monte Carlo with Directed Loops
- Stochastic series expansion method with operator-loop update
- Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
- Berry phase effect in anomalous thermoelectric transport
- Theory of Thermal Hall Effect in Quantum Magnets
- Computational Studies of Quantum Spin Systems
- The Hubbard Model
- Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
- Suppression of the Persistent Spin Hall Current by Defect Scattering
- Worm algorithms for classical statistical models
- Universality of the Mott-Ioffe-Regel limit in metals
- Bad metallic transport in a cold atom Fermi-Hubbard system
- Rotational motion of magnon and thermal Hall effect
- Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
- Energy Magnetization and Thermal Hall Effect
- Unusual thermal Hall effect in a Kitaev spin liquid candidate -RuCl
- Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
- Visibility of the Amplitude (Higgs) Mode in Condensed Matter
- Stochastic series expansion method for quantum Ising models with arbitrary interactions
- Berry Curvature and Phonon Hall Effect
- Phonons become chiral in the pseudogap phase of cuprates
- High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
- Phonon thermal Hall effect in strontium titanate
- Towards a statistical theory of transport by strongly-interacting lattice fermions
- Strange metallicity in the doped Hubbard model
- Accessing the dynamics of large many-particle systems using Stochastic Series Expansion
- Disorder effects in the AHE induced by Berry curvature
- Sign reversing Hall effect in atomically thin high temperature superconductors
- Progress on stochastic analytic continuation of quantum Monte Carlo data
- Analytical and numerical study of hardcore bosons in two dimensions
- Spin transport of weakly disordered Heisenberg chain at infinite temperature
- Small-angle impurity scattering and the spin Hall conductivity in 2D systems
- Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a DMFT Perspective
- Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model
- "Bad Metal" Conductivity of Hard Core Bosons
- Quantum Kinetic Theory of the Chiral Anomaly
- Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
- Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model
- Dynamics and Conductivity Near Quantum Criticality
- Many-body Chern number without integration
- A Sum Rule for Thermal Conductivity and Dynamical Thermal Transport Coefficients in Condensed Matter -I
- Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective
- Non-vanishing spin Hall currents in disordered spin-orbit coupling systems
- Charge Dynamics in the Planar t-J Model
- The Hall Number of Strongly Correlated Metals
- Kerr effect as evidence of gyrotropic order in the cuprates - revisited
- Fate of a topological invariant for correlated lattice electrons at finite temperature
- Topological Transitions for Lattice Bosons in a Magnetic Field
- Quantum kinetic equation in phase-space textured multiband systems
- Equilibrium Formulae for Transverse Magneto-transport of Strongly Correlated Metals
- Universality and Critical Exponents of the Fermion Sign Problem
- DC Hall coefficient of the strongly correlated Hubbard model
- Deconfinement of Mott Localized Electrons into Topological and Spin-Orbit Coupled Dirac Fermions
- Vortex Dynamics and Hall Conductivity of Hard Core Bosons
- Hall coefficient of semimetals
- DSQSS: Discrete Space Quantum Systems Solver
- Vortex quantum dynamics of two dimensional lattice bosons
- Hall effect in doped Mott insulator: DMFT-approximation
- Fast and stable determinant quantum Monte Carlo
- Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model
- Hall anomaly and moving vortex charge in layered superconductors
- Metallic transport of hard core bosons
- Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator
- Memory Function Approach to Correlated Electron Transport: A Comprehensive Review
- A flexible class of exact Hubbard-Stratonovich transformations
- The directed-loop algorithm
- Perturbative solution of fermionic sign problem in lattice Quantum Monte Carlo
- Degeneracy-projected polarization formulas for Hall-type conductivities