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The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are…
We consider the problem of fermions interacting with gapless long-wavelength collective bosonic modes. The theory describes, among other cases, a ferromagnetic quantum-critical point (QCP) and a QCP towards nematic ordering. We construct a…
We have performed Brownian dynamics simulations on melting of two-dimensional colloidal crystal in which particles interact with Yukawa potential. The pair correlation function and bond-orientational correlation function was calculated in…
I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the…
A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state. We use adiabaticity arguments and numerical…
We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting…
We explore the parameter space for processes with fermionic flavor violation within the 2HDM type III, processes of Flavor Changing Neutral Currents are present at LO as dynamics beyond the Standard Model are included. We analyze the…
We study the interplay among disorder, RKKY and Kondo interactions in {\it f}-electron alloys. We argue that the non-Fermi liquid behavior observed in these systems is due to the existence of a Griffiths phase close to a quantum critical…
Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ($N$$\ge$$2$) fermions per site with random interactions and hoppings between…
We analyze the normal phase of the attractive Hubbard model within dynamical mean-field-theory. We present results for the pair-density, the spin-susceptibility, the specific heat, the momentum distribution, and for the quasiparticle…
Quantum criticality plays a central role in understanding non-Fermi liquid behavior and unconventional superconductivity in strongly correlated systems. In this review, we explore the quantum critical Eliashberg theory, which extends…
We address the outstanding problem of electron pairing in the presence of strong Coulomb repulsion at small to moderate values of the Coulomb parameter, $r_s \lesssim 2$, and demonstrate that the pseudopotential framework is fundamentally…
We study a system of fermions interacting with a scalar field, in 4+1 dimensions where the 5th dimension is compactified, using an exact functional method, where quantum fluctuations are controlled by the amplitude of the bare fermion mass.…
We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $\lambda$. Using the hyper-netted chain closure to the Ornstein-Zernike…
This work deals with the behavior of fermions in the background of kinklike structures in the two-dimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the…
Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we…
We establish through analytical and numerical studies of thermodynamic quantities for noninteracting atomic gases that the isotropic three-dimensional spin-orbit coupling, the Weyl coupling, induces interaction which counters "effective"…
We analyse a class of SYK models whose Hamiltonian is the sum of two SYK Hamiltonians with different numbers of fermions $q, \tilde q$ in each interaction. We consider both Euclidean and Lorentzian probes of the quantum system in the large…
The Sachdev-Ye-Kitaev (SYK) model provides an analytically tractable framework for exotic strongly correlated phases where conventional paradigms like Landau's Fermi liquid theory collapse. This review offers a pedagogical introduction to…
A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in…