We investigate the effects of a time-periodic, non-hermitian, PT -symmetric perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We demonstrate that when the perturbation frequency is close to one of the system resonances, even a vanishingly small perturbation leads to PT symmetry breaking. We also find a restored PT -symmetric phase at high frequencies, and at moderate perturbation strengths, we find multiple frequency windows where PT -symmetry is broken and restored. Our results imply that the PT -symmetric Rabi problem shows surprisingly rich phenomena absent in its hermitian or static counterparts. Introduction.A two-level system coupled to a sinusoidally varying potential is a prototypical example of a time-dependent, exactly solvable Hamiltonian, with profound implications to atomic, molecular, and optical physics [1]. When the frequency of perturbation ω is close to the characteristic frequency ∆ of the two-level system -near resonance -the system undergoes complete population inversion for an arbitrarily small strength γ of the potential [2]. The implications of this result to spin magnetic resonance, Rabi flopping [3], and its generalization, namely the Jaynes-Cummings model [4,5], have been extensively studied over the past half century [6,7]. Surprisingly, the quantum Rabi problem, where the full quantum nature of the perturbing bosonic field is taken into account, has only been recently solved [8].The two-level model is useful because it is applicable to many-level systems when the perturbation frequency is close to or resonant with a single pair of levels. As the detuning away from resonance |∆ − ω| increases, the perturbation strength necessary for population inversion increases linearly with it; in a many-level system, with increased potential strength, transitions to other levels have to be taken into account and the resultant problem is not exactly solvable. Therefore, understanding the behavior of a system in the entire parameter space (γ, ω) requires analytical and numerical approaches. All of these studies are restricted to hermitian potentials.In recent years, discrete Hamiltonians with a hermitian tunneling term H 0 and a non-hermitian perturbation V that are invariant under combined parity and timereversal (PT ) operations have been extensively investigated [9][10][11][12][13][14][15][16]. The spectrum λ of a PT -symmetric Hamiltonian is real when the strength γ of the non-hermitian perturbation is smaller than a threshold γ P T set by the hermitian tunneling term. Traditionally, the emergence of complex-conjugate eigenvalues that occurs when the threshold is exceeded, γ > γ P T , is called PT symmetry breaking [17][18][19]. It is now clear that PT -symmetric Hamiltonians represent open systems with balanced gain and loss, and PT symmetry breaking is a transition from a quasiequilibrium state (PT -symmetric state) to

We study the problem of underscreened Kondo physics in an interacting electronic system modeled by a Luttiger Liquid (LL). We find that the leading temperature dependence of thermodynamical quantities like the specific heat, spin susceptibility are Fermi Liquid like in nature. However, anomalous power law exponents are seen in the subleading terms. We also discuss possible realizations through single and double quantum dot configurations coupled to LL leads and its consequences for electronic transport. The leading low temperature transport behavior is seen to exhibit in general, non Fermi liquid LL behavior unlike the thermodynamical quantities.Comment: 8 pages, 1 figure, final versio

We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous sub-diffusive scaling behaviour in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest and next-nearest neighbour hopping using analytical and numerical methods. The global scaling shows the existence of a 'causal light-cone' corresponding to excitations travelling with a velocity smaller than a maximal 'light velocity'. Maximal fronts moving with fixed 'light velocity' bound the causal cone. The front regions spread with time sub-diffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest neighbour hopping strength, there is a transition from a phase with one 'causal cone' to a phase with two nested 'causal cones' and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single particle quantum walk on the one dimensional lattice already captures the many body physics of a spin chain system. In particular, we suggest that the time evolution of a single particle quantum walk on the one dimensional lattice with an initially localized state is equivalent to the time evolution of a domain wall initial state in a corresponding spin chain system. probability density p(n, t) = |ψ(n, t)| 2 scales as

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We study the interplay of electric and magnetic order in the one dimensional Heisenberg spin-1/2 XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (D-M) interaction and with longitudinal and transverse magnetic fields, interpreting the D-M interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped Néel phase with antiferromagnetic (AF) order, gapped saturated phase and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the Néel phase(even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.