Current fidelity susceptibility and conductivity in one-dimensional lattice models with open and periodic boundary conditions

We study, both numerically and analytically, the finite size scaling of the fidelity susceptibility \chi_{J} with respect to the charge or spin current in one-dimensional lattice models, and relate it to the low-frequency behavior of the corresponding conductivity. It is shown that in gapless systems with open boundary conditions the leading dependence on the system size L stems from the singular part of the conductivity and is quadratic, with a universal form \chi_{J}= 7KL^2 \zeta(3)/2\pi^4 where K is the Luttinger liquid parameter. In contrast to that, for periodic boundary conditions the leading system size dependence is directly connected with the regular part of the conductivity (giving alternative possibility to study low frequency behavior of the regular part of conductivity) and is subquadratic, \chi_{J} \propto L^\gamma(K), (with a K dependent constant \gamma) in most situations linear, \gamma=1. For open boundary conditions, we also study another current-related quantity, the fidelity susceptibility to the lattice tilt \chi_{P} and show that it scales as the quartic power of the system size, \chi_{P}=31KL^4 \zeta(5)/8 u^2 \pi^6, where u is the sound velocity. We comment on the behavior of the current fidelity susceptibility in gapped phases, particularly in the topologically ordered Haldane state.Comment: 11 pages, 7 eps figure

Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice

We study the magnetic phase diagram of spin-3/2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large on-site repulsion the system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We analyze the Sp(N) spin model with the help of the large-N field-theoretical approach and show that the effective theory corresponds to the Sp(N) extension of the CP^{N-1} model, with the Lorentz invariance generically broken. We obtain the renormalization flow of the model couplings and show that although the Sp(N) terms are seemingly irrelevant, their presence leads to a renormalization of the CP^{N-1} part of the action, driving a phase transition. We further consider the influence of the external magnetic field (the quadratic Zeeman effect), and present the qualitative analysis of the ground state phase diagram.Comment: 10 Revtex pages, 5 figures; (v2) corrected the last paragraph in Appendix B and some typos; (v3) added references, extended discussion of the phase diagra

Ultra-cold bosons in zig-zag optical lattices

Ultra-cold bosons in zig-zag optical lattices present a rich physics due to the interplay between frustration, induced by lattice geometry, two-body interaction and three-body constraint. Unconstrained bosons may develop chiral superfluidity and a Mott-insulator even at vanishingly small interactions. Bosons with a three-body constraint allow for a Haldane-insulator phase in non-polar gases, as well as pair-superfluidity and density wave phases for attractive interactions. These phases may be created and detected within the current state of the art techniques.Comment: 8 pages, 9 figure

Field-induced phase transitions of repulsive spin-1 bosons in optical lattices

We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, being in excellent agreement with our numerical calculations for one-dimensional systems. Our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.Comment: 4 pages, 2 figure

Exploring spin-orbital models with dipolar fermions in zig-zag optical lattices

Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.Comment: 4 pages + supplementary materia

Susceptibility at the edge points of magnetization plateau of 1D electron/spin systems

We study the behavior of magnetization curve as a function of magnetic field in the immediate vicinity of the magnetization plateaus of 1D electron systems within the bosonization formalism. First we discuss the plateau that is formed at the saturation magnetization of 1D electron system. Interactions between electrons we treat in the lowest order of perturbation. We show that for isolated systems, where total number of electrons is not allowed to vary, magnetic susceptibility stays always finite away of half filling. Similar statement holds for many other magnetization plateaus supporting nonmagnetic gapless excitations encountered in 1D electron/spin systems in the absence of special symmetries or features responsible for the mode decoupling. We demonstrate it on example of the plateaus at irrational values of magnetization in doped modulated Hubbard chains. Finally we discuss the connection between the weak coupling description of saturation magnetization plateau and strong coupling description of zero magnetization plateau of attractively interacting electrons/ antiferromagnetically interacting spin 1 Bosons.Comment: 10 pages, 3 figures. To appear in Phys. Rev.

Quantum dimer phases in a frustrated spin ladder: Effective field theory approach and exact diagonalization

The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.Comment: 10 pages RevTex4, 7 figures; final version with some small extensions; to appear in Phys. Rev.