Topological Phases of Fermionic Ladders with Periodic Magnetic Fields

In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultra-cold Fermi gases in ladder-like optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, non-zero Chern numbers, Hofstadter-like-butterfly spectrum, and a complete phase diagram of non-interacting fermionic ladders.Comment: 5 pages, 5 figure

Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin-12\frac{1}{2} chain

Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3\delta_{a,b}-1) \ln^2r /(12 \pi^4 r^4)$, and estimate the numerical prefactor as $d\simeq 0.067$. The relevance of our results for ground state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.Comment: 10 pages, 2 figure

The optimal frequency window for Floquet engineering in optical lattices

The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $\tau$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $\tau$. As a main result, we find that, when increasing the lattice depth, $\tau$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.Comment: 11 pages, 8 figure

Aufbau Principle for Non-Hermitian Systems

We develop a generalized Aufbau principle for non-Hermitian systems that allows for building up the configurations of indistinguishable particles. The Aufbau rule of non-Hermitian systems is unexpectedly shown to be identical to that developed in Hermitian systems when the real parts of the complex energy levels are considered. We derive full many-body energy spectra of the fermionic and bosonic Hatano-Nelson models as examples by filling single-particle energy levels in the momentum space. For open boundary conditions, we show that many-body non-Hermitian skin effects persist in all many-body eigenstates for both fermions and bosons. Furthermore, we find surprisingly that the ground state of bosons is an anomalous Bose-Einstein condensation with all of the particles simultaneously localizing in both the real and momentum space beyond the Heisenberg uncertainty principle. For periodic boundary conditions, we show that hard-core bosons cannot be mapped to fermions. This work establishes a general framework for understanding the many-body physics of non-Hermitian systems, revealing rich unique non-Hermitian many-body physics.Comment: 6 pages, 4 figure

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a non-trivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner- to vortex-superfluid transition, and a non-trivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a non-chiral and a chiral superfluid, both characterized by non-trivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.Comment: 5 pages, 4 figure

Spin-orbital models in optical lattices

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Quantum criticality in interacting bosonic Kitaev-Hubbard models

Motivated by recent work on the non-Hermitian skin effect in the bosonic Kitaev-Majorana model, we study the quantum criticality of interacting bosonic Kitaev-Hubbard models on a chain and a two-leg ladder. In the hard-core limit, we show exactly that the non-Hermitian skin effect disappears via a transformation from hard-core bosonic models to spin-1/2 models. We also show that hard-core bosons can engineer the Kitaev interaction, the Dzyaloshinskii-Moriya interaction and the compass interaction in the presence of the complex hopping and pairing terms. Importantly, quantum criticalities of the chain with a three-body constraint and unconstrained soft-core bosons are investigated by the density matrix renormalization group method. This work reveals the effect of many-body interactions on the non-Hermitian skin effect and highlights the power of bosons with pairing terms as a probe for the engineering of interesting models and quantum phase transitions.Comment: 9 pages, 6 figure