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arXiv:2101.06420 · Physical review. B./Physical review. B

Localization dynamics from static and mobile impurities

Ephraim Bernhardt, Fan Yang, Karyn Le Hur

Published Sep 7, 2021• 1 citation
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Abstract

We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}(1)$ gauge field or a uniform magnetic field. Impurities are described through two-state systems, which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local ${\mathbb{Z}}_{2}$ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N\'eel state.

DOI
10.1103/physrevb.104.115113

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We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a U(1)\mathbb{U}(1)U(1) gauge field or a uniform magnetic field. Impurities are described through two-state systems, which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local Z2{\mathbb{Z}}_{2}Z2​ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N'eel state.
We study the superfluid response and localization dynamics from impurities and gauge theories. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a U(1)\mathbb{U}(1)U(1) gauge field or a uniform magnetic field. Impurities are described through two-state systems which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a Z2\mathbb{Z}_2Z2​ symmetry for static impurities and we formulate a correspondence to Z2\mathbb{Z}_2Z2​ gauge theories for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we analyse the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N\' eel state.
In this thesis, we work on three problems. In the first problem, we work on a local time-dependent potential in a one-dimensional interacting bath. This work is motivated by cold atomic experiments, where one can shake the ultracold systems by using a time-dependent potential. We use linear response theory, bosonization, and renormalization group to compute the energy deposition in the one-dimensional bath by the time-dependent potential. We find that the energy deposition both for weak and strong coupling regimes shows a power-law behavior on the frequency of oscillation, and shows a different power-law exponent in strong and weak coupling limit. In the second problem, we work on the dynamics of a mobile impurity in a two-leg bosonic ladder. The theoretical and experimental studies of a mobile impurity in a one-dimensional bath in context of ultracold systems motivate this work. We confine the impurity to move in one of the legs of the ladder. We combine bosonization, renormalization group, and density matrix renormalization group to understand the dynamics of the impurity. We compute the Green's function of the impurity both theoretically and numerically. For a small interaction between the impurity and the bath, we find theoretically that the Green's function of the impurity decays as a power-law, and our numerical results show a good agreement with analytical result. Furthermore, we also give an analytical result of the Green's function for an infinite interaction, we find again that the Green's function decays as a power-law, and shows a good agreement with numerical results. Moreover, finally we give a semi-analytical expression for the power-law exponent at zero momentum as a function of interaction, again in good agreement with the numerical results. In the third problem, we are again investigating the dynamics of a mobile impurity in a two-leg bosonic ladder, but in this case, the impurity also tunnels in both longitudinal and transverse directions. We use similar methods than for the second problem. We compute the Green's function in the bonding and the anti-bonding modes of the impurity. The Green's function in the anti-bonding mode decays as power-law at small momentum and small interaction, while the Green's function in the bonding decays exponentially, and our numerical results show a good agreement with analytical ones.
Abstract We investigate the ground state properties of interacting bosons on a triangular ladder subject to an artificial magnetic field. By means of the mean-field approximation, rich phases are revealed in the limit of weak interaction and large bosons occupation per site, including the Meissner superfluid, vortex superfluid, biased chiral superfluid (C-SF), C-SF and insulating phases. The quantum phases can be precisely identified and the underlying physics of phase transitions can be clarified by utilizing order parameters based on the atomic density, the effective rung current, and the current asymmetry ratio. Meanwhile, the phase transition of the system can be effectively controlled by adjusting the rung-to-leg coupling ratio, the magnetic flux and the atomic interaction. Furthermore, using Bogoliubov theory, we have mapped the stability phase diagram across all parameters, and clarified the interdependence between superfluidity and the dispersion relation. The excitation spectrum, which effectively describes the system’s energetic stability, is governed by the rung-to-leg coupling ratio, the magnetic flux, and the atomic interaction. Numerical simulations validate the dynamical instability of the system. This work offers a theoretical foundation for identifying new quantum phases exhibited by ultracold atoms in optical lattices and new experimental approaches for achieving system superfluidity.
We investigate the quench dynamics of interacting bosons on a two-leg ladder in presence of a uniform Abelian gauge field. The model hosts a variety of emergent quantum phases, and we focus on the superfluid biased-ladder phase breaking the Z2Z_{2}Z2​ symmetry of two legs. We observe an asymmetric spreading of vortex current and particle density, i.e., the current behaves particle-like on the right and wave-like on the left, indicating spontaneous breaking of the spatial inversion symmetry. By decreasing the repulsion strength, it is found the particle-like current is more robust than the wave-like one. The evolution of entanglement entropy manifests logarithmic growth with time suggesting many-body localization matters.
We introduce generic bosonic models exemplifying that chiral Meissner currents can persist in insulating phases of matter. We first consider interacting bosons on a two-leg ladder. The total density sector can be gapped in a bosonic Mott insulator at odd-integer filling, while the relative density sector remains superfluid due to interchain hopping. Coupling the relative density to gauge fields yields a pseudospin Meissner effect. We show that the same phase arises if the bosons are replaced by spinful fermions confined in Cooper pairs, and find a dual fermionic Mott insulator with spinon currents. We prove that, by tuning the mean density, the Mott insulator with Meissner currents turns into a low-dimensional bosonic $\ensuremath{\nu}=\frac{1}{2}$ Laughlin state for strong enough repulsive interactions across the ladder rungs. We finally discuss extensions to multileg ladders and bilayers in which spinon superfluids with Meissner currents become possible. We propose two experimental realizations, one with ultracold atoms in the setup of Atala et al. [Nat. Phys. 10, 588 (2014)] and another with Josephson junction arrays. We also address a Bose-Fermi mixture subject to a magnetic field in connection with the pseudogap phase of high-Tc{T}_{c}Tc​ cuprates.
We analyze the behavior of a mobile quantum impurity, restricted to a one-dimensional motion, in a bath formed by a two-leg bosonic ladder through a combination of field theory [Tomonaga-Luttinger liquid (TLL)] and numerical (density-matrix renormalization group) techniques. We compute the Green's function of the impurity as a function of time at different momenta. We find a power-law decay at zero momentum, which signals the breakdown of a quasiparticle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, the impurity experiences the ladder as a single channel one-dimensional bath, but with an effective coupling reduced by a factor of 2\sqrt{2}2​. We compare the numerical results for the exponent at zero momentum with a semianalytical expression, initially established for the chain, and find excellent agreement without adjustable parameters. We find an increase of the exponent with increasing transverse tunneling in the bath. At small tunneling, the exponent is compatible with the TLL prediction, while larger tunneling shows strong deviations. Finally, we show that, as a function of the momentum of the impurity, two different regimes of decay of the Green's function exist, similar to the single chain case. The power-law regime occurs for small momentum, while at large momentum the Green's function shows a faster decay, corresponding to the one expected in a polaronic regime. In this last regime, we compute the lifetime of the polaron numerically. We compute the critical momentum marking the transition between these two regimes. We compare with analytical predictions based on the structure factor of the bath and find good agreement with the numerical results. Finally, we discuss the consequences of our results for cold atomic experiments.