The density-matrix renormalization group is employed to investigate a harmonically trapped imbalanced Fermi condensate based on a one-dimensional attractive Hubbard model. The obtained density ...profile shows a flattened population difference of spin-up and spin-down components at the center of the trap, and exhibits phase separation between the condensate and unpaired majority atoms for a certain range of the interaction and population imbalance P. The two-particle density matrix reveals that the sign of the order parameter changes periodically, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to the quasicondensate up to at least P approximately 0.8. Possible experimental situations to test our predictions are discussed.
A
bstract
In this paper, we analyze a proposed gravity dual to a SU(
N
) Bose-Hubbard model, as well as construct a holographic dual of a SU(
N
) Fermi-Hubbard model from D-branes in string theory. ...In both cases, the SU(
N
) is dynamical, i.e. the hopping degrees of freedom are strongly coupled to SU(
N
) gauge bosons which themselves are strongly interacting. The vacuum expectation value (VEV) of the hopping term (i.e. the hopping energy) is analyzed in the gravity dual as a function of the bulk mass of the field dual to the hopping term, as well as of the coupling constants of the model. The bulk mass controls the anomalous dimension (i.e. the critical exponent) of the hopping term in the SU(
N
) Bose-Hubbard model. We compare the hopping energy to the corresponding result in a numerical simulation of the ungauged SU(
N
) Bose-Hubbard model. We find agreement when the hopping parameter is smaller than the other couplings. Our analysis shows that the kinetic energy increases as the bulk mass increases, due to increased contributions from the IR. The holographic Bose-Hubbard model is then compared with the string theory construction of a SU(
N
) Fermi-Hubbard model. The string theory construction makes it possible to describe fluctuations around a half-filled state in the supergravity limit, which map to
O
1
occupation number fluctuations in the Fermi-Hubbard model at half filling. Finally, the VEV of the Bose-Hubbard model is shown to agree with the one of the fermionic Hubbard model with the help of a two-site version of the Jordan-Wigner transformation.
Abstract
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search ...for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.
Understanding how and whether local perturbations can affect the entire quantum system is a fundamental step in understanding non-equilibrium phenomena such as thermalization. This knowledge of ...non-equilibrium phenomena is applicable for quantum computation, as many quantum computers employ non-equilibrium processes for computations. In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators in the one-dimensional Ising model with magnetic field and the disordered Heisenberg model to study the properties of quantum circuits. In the Ising model, the early-time evolution qualitatively follows an effective light cone picture, and the late-time value is well described by Page’s value for a random pure state. In the Heisenberg model with strong disorder, we find that many-body localization prevents the information from propagating and being delocalized. We also find an effective Ising Hamiltonian that describes the time evolution of bi- and tripartite operator mutual information for the Heisenberg model in the large disorder regime.
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random ...matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.
Interacting-Holstein and extended-Holstein bipolarons Chakraborty, Monodeep; Tezuka, Masaki; Min, B. I.
Physical review. B, Condensed matter and materials physics,
01/2014, Letnik:
89, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Employing the recently developed self-consistent variational basis generation scheme, we have investigated the bipolaron-bipolaron interaction within the purview of the Holstein-Hubbard and the ...extended-Holstein-Hubbard (F2H) models on a discrete one-dimensional lattice. The density-matrix renormalization group method has also been used for the Holstein-Hubbard model. We have shown that there exists no bipolaron-bipolaron attraction in the Holstein-Hubbard model. In contrast, we have obtained clear-cut bipolaron-bipolaron attraction in the F2H model. Composite bipolarons are formed above a critical electron-phonon coupling strength, which can survive the finite Hubbard U effect. We have constructed the phase diagram of F2H polarons and bipolarons, and discussed the phase separation in terms of the formation of composite bipolarons.
We have found an error in section 6 of this paper. In that section we gave a heuristic argument estimating the ramp time of Hamiltonian systems by assuming that the slowest decay in eq. (105) was ...that of simple operators.
We study level statistics of a generalized Sachdev-Ye-Kitaev (SYK) model with two-body and one-body random interactions of finite range by exact diagonalization. Tuning the range of the one-body ...term, while keeping the two-body interaction sufficiently long ranged, does not alter substantially the spectral correlations, which are still given by the random matrix prediction typical of a quantum chaotic system. However, a transition to an insulating state, characterized by Poisson statistics, is observed by reducing the range of the two-body interaction. Close to the many-body metal-insulator transition, we show that spectral correlations share all features previously found in systems at the Anderson transition and in the proximity of the many-body localization transition. Our results suggest the potential relevance of SYK models in the context of many-body localization. It also offers a starting point for the exploration of a gravity dual of this phenomenon which we speculate to be related to the Hawking-Page transition.
In this work, we propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into ...a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).
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