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Register a new userQuantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians
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We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.
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Concentrating on bosonic lattice systems, we ask whether and how Excited State Quantum Phase Transition (ESQPT) singularities occur in condensed matter systems with ground state QPTs. We study in particular the spectral singularities above the ground-state phase diagram of the boson Hubbard model. As a general prerequisite, we point out the analogy between ESQPTs and van Hove singularities (vHss).
Considering nonintegrable quantum Ising chains with exponentially decaying interactions, we present matrix product state results that establish a connection between low-energy quasiparticle excitations and the kind of nonanalyticities in the Loschmidt return rate. When domain walls in the spectrum of the quench Hamiltonian are energetically favored to be bound rather than freely propagating, anomalous cusps appear in the return rate regardless of the initial state. In the nearest-neighbor limit, domain walls are always freely propagating, and anomalous cusps never appear. As a consequence, our work illustrates that models in the same equilibrium universality class can still exhibit fundamentally distinct out-of-equilibrium criticality. Our results are accessible to current ultracold-atom and ion-trap experiments.
We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.
We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard phases, and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point changes dramatically. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.
We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with the increasing of disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At $f=1$, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the $f=5/2$ fermionic Moore-Read cousin.
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