Karlis Mikelsons

Quantum criticality due to incipient phase separation in the two-dimensional Hubbard model

We investigate the two-dimensional Hubbard model with next-nearest-neighbor hopping, t, using the dynamical cluster approximation. We confirm the existence of a first-order phase-separation transition terminating at a second-order critical point at filling nct and temperature Tpst. We find that as t approaches zero, Tpst vanishes and nct approaches the filling associated with the quantum critical point separating the Fermi liquid from the pseudogap phase. We propose that the quantum critical point under the superconducting dome is the zero-temperature limit of the line of second-order critical points.

Nonlocal effects on magnetism in the diluted magnetic semiconductor Ga1-xMnxAs.

The magnetic properties of the diluted magnetic semiconductor Ga1-xMnxAs are studied within the dynamical cluster approximation. We use the k x p Hamiltonian to describe the electronic structure of GaAs with spin-orbit coupling and strain effects. We show that nonlocal effects are essential for explaining the experimentally observed transition temperature and saturation magnetization. We also demonstrate that the cluster anisotropy is very strong and induces rotational frustration and a cube-edge direction magnetic anisotropy at low temperature. With this, we explain the temperature-driven spin reorientation in this system.

Thermodynamics of the quantum critical point at finite doping in the two-dimensional Hubbard model studied via the dynamical cluster approximation

We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approximation. We use continuous time quantum Monte Carlo as a cluster solver to avoid the systematic error which complicates the calculation of the entropy and potential energy (double occupancy). We find that at a critical filling, there is a pronounced peak in the entropy divided by temperature,

Thermalization of field driven quantum systems

S/T

Quasiuniversal Transient Behavior of a Nonequilibrium Mott Insulator Driven by an Electric Field

, and in the normalized double occupancy as a function of doping. At this filling, we find that specific heat divided by temperature,

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory.

C/T

Dynamical Cluster Approximation

, increases strongly with decreasing temperature and kinetic and potential energies vary like

Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods.

{T}^{2}\text{ }\text{ln}\text{ }T

Feshbach modulation spectroscopy of the Fermi-Hubbard model

. These are all characteristics of quantum critical behavior.

Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model

There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinite-temperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the Falicov-Kimball model (which does not), we find both exhibit scenarios (i–iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role.