Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using the center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sublattice symmetry. Under the condition of the hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flatband, which is the origin of the rung-pair localization. We also study the multiparticle dynamics of the Bose-Hubbard ladder model, which is beyond the single-particle picture. In this case, we find that the localization can still survive despite the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flatband, which is induced by on-site interaction and specific lattice symmetry.
Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using the center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sublattice symmetry. Under the condition of the hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flatband, which is the origin of the rung-pair localization. We also study the multiparticle dynamics of the Bose-Hubbard ladder model, which is beyond the single-particle picture. In this case, we find that the localization can still survive despite the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flatband, which is induced by on-site interaction and specific lattice symmetry.
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.
Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.
The phenomenology of many-body localization (MBL) develops mainly from tackling the one-dimensional spin or fermion systems. The situation when interacting bosons get clustered in a random potential remains less explored. Using numerical quantum quenches with special emphasis on the integration of both symmetry and energy resolutions, we comprehensively study the dynamics of symmetry-resolved entanglement in a disordered Bose-Hubbard (dBH) model, concentrating on the two types of inhomogeneous initial states to target the lower- and higher-energy sections of its dynamical phase diagram. (i) Motivated by the recent experiment [A. Lukin et al., Science 364, 256 (2019)] which focused on the lower-energy dynamical behaviors of the dBH chain, we first show that at low energies, for a thermalizing state, although the second law of thermodynamics prohibits the decrease of the total entropy over time, for part of the channel-resolved entropies, a long-term entropic reduction may arise at weak disorder. (ii) A companion channel-resolved analysis at strong disorder further hints that the prior observed double-logarithmic growth of the number entropy might not directly indicate the breakdown of MBL in spin or fermion chains, providing a refreshing perspective on this major controversy in the community. (iii) From time-evolving the line-shape low-energy product state, we subsequently reveal an abrupt formation of a novel ``entropy imbalance pattern'' across the different symmetry channels. Intriguingly, this imbalance melts in the strong-disorder limit. We conjecture that the melting of the entropic pattern, together with the freezing of a concurrent particle-density wave, embodies a dual trait inherent to MBL. (iv) Conversely, the higher-energy section of the dynamical phase diagram is where the dBH model differs most significantly from the spin or fermion systems. This parametric space was not included in the previous literature. Specifically, we find a cluster MBL regime, unique to the Bose statistics, emerging from the higher-energy section. This cluster MBL regime, realizable even at weak disorder, does not appear to suffer from the finite-size drift and is distinguished by its absence of the hallmark of MBL---the unbounded growth of the entanglement entropy. Our theoretical predictions are, by and large, testable via the present experimental facilities.
We study the quench dynamics of two bosons possessing on-site repulsive interaction on a two-leg ladder and show that the presence of uniform flux piercing through the plaquettes of the ladder favors the localization of the bound states in the dynamics. We find that, when the two bosons are symmetrically initialized on the edge rung of the ladder, they tend to edge-localize in their quantum walk, a phenomenon which is not possible in the absence of flux. However, when the bosons are initialized on the bulk rung they never localize and exhibit linear spreading in their quantum walk. Interestingly, however, we find that, in the later case, a finite flux favors localization of the bulk bound states in the presence of sufficiently weak quasiperiodic disorder, which is otherwise insufficient to localize the particles in the absence of flux. In both cases, we obtain that the localization in the dynamics strongly depends on the combined effect of the flux and interaction strengths, as a result of which we obtain a signature of reentrant delocalization as a function of flux (interaction) for fixed interaction (flux) strengths.
Many-body localization of a disorder interacting boson system in one dimension is studied numerically at the filling factor being one-half, in terms of level statistics, local compressibility, correlation function and entanglement entropies. The von Neumann entanglement entropy is decoupled into a particle number entropy and a configuration entropy. An anomalous volume-law behavior is found for the configuration entanglement entropy to confirm a recent experimental observation [A. Lukin, M. Rispoli, R. Schittko, et al., Science 364, 256 (2019)] for sufficient strong disorder, while the particle number entropy fulfills an area-law corresponding to the total entropy for disordered spin chain. The localization length are extracted from a two-body correlation function for many-body localization states and corresponding time-evolutions states as well. A phase diagrams is established with consisting of an ergodic thermalized region and a many-body-localization region in a parameter space of the disorder strength and the energy density. Two regions are separated by a many-body mobility edge deducted from the standard deviation of the particle-number entanglement entropy, which appears consistent with that based on the localization length. Slow dynamics characterized by a logarithmic time-dependence is explicitly shown for both the particle number entropy and the configuration entropy in an intermediate regime of their time-evolutions, which does not show up in the Anderson localization case, i.e. non-interacting disorder systems.