420 research outputs found
Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory
Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT+DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT+ED simulations
Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator
Computing superconducting properties starting from an exactly solvable model
for a doped Mott insulator stands as a grand challenge. We have recently shown
that this can be done starting from the Hatsugai-Kohmoto (HK) model which can
be understood generally as the minimal model that breaks the non-local symmetry of a Fermi liquid, thereby constituting a new quartic fixed point
for Mott physics [Phillips et al., Nature Physics 16, 1175 (2020); Huang et
al., Nature Physics (2022)]. In the current work, we compute the
thermodynamics, condensation energy, and electronic properties such as the NMR
relaxation rate and ultrasonic attenuation rate. Key differences arise
with the standard BCS analysis from a Fermi liquid: 1) the free energy exhibits
a local minimum at where the pairing gap turns on discontinuously above a
critical value of the repulsive HK interaction, thereby indicating a
first-order transition, 2) a tri-critical point emerges, thereby demarcating
the boundary between the standard second-order superconducting transition and
the novel first-order regime, 3) Mottness changes the sign of the quartic
coefficient in the Landau-Ginzburg free-energy fuctional relative to that in
BCS, 4) as this obtains in the strongly interacting regime, it is Mott physics
that underlies the generic first-order transition, 5) the condensation energy
exceeds that in BCS theory suggesting that multiple Mott bands might be a way
of enhancing superconducting, 6) the heat-capacity jump is non-universal and
increases with the Mott scale, 7) Mottness destroys the Hebel-Slichter peak in
NMR, and 8) Mottness enhances the fall-off of the ultrasonic attenuation at the
pairing temperature . As several of these properties are observed in the
cuprates, our analysis here points a way forward in computing superconducting
properties of strongly correlated electron matter.Comment: accepted in PR
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