Related papers: Hermitian--to--quasi-Hermitian quantum phase trans…
We show that degenerate four-wave mixing (FWM) in nonlinear optics can be described by an effective Hamiltonian that is pseudo-Hermitian, which enables a transition between a pseudo-Hermitian phase with real eigenvalues and a broken…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
Detailed description of nuclei necessitates model Hamiltonians which break most dynamical symmetries. Nevertheless, generalized notions of partial and quasi dynamical symmetries may still be applicable to selected subsets of states, amidst…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
We consider the possibility of topological quantum phase transitions of ultracold fermions in optical lattices, which can be studied as a function of interaction strength or atomic filling factor (density). The phase transitions are…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
Synthetic nonconservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting…
We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We describe recent experimental evidence that points to a relation between…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
We present a new theoretical approach for the study of the phase diagram of interacting quantum particles: bosons, fermions or spins. In the neighborhood of a phase transition, the expected renormalization group structure is recovered both…
During the early history of unitary quantum theory the Kato's exceptional points (EPs, a.k.a. non-Hermitian degeneracies) of Hamiltonians $H(\lambda)$ did not play any significant role, mainly due to the Stone theorem which firmly connected…
We study quantum phase transitions in Bose-Fermi mixtures driven by interspecies interaction in the quantum Hall regime. In the absence of such an interaction, the bosons and fermions form their respective fractional quantum Hall (FQH)…
We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric superconducting qubits chains described by a transverse-field Ising spin model. A non-Hermitian…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
We study state conversion in parity-time (PT) symmetry broken non-Hermitian two level system. We construct a theory and explain underlying mechanism for state conversion and define adiabatic evolutions in non-Hermitian systems. The…
Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the…
The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be…
The interplay between superconductivity and environmental dissipation, effectively captured by non-Hermitian Hamiltonian, is a new frontier for exotic quantum phases. We explore a PT-symmetric non-Hermitian superconductor with balanced gain…
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…