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arXiv:2301.09807 · Physical Review A

Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models

Mathias Mikkelsen, Ippei Danshita

Published Apr 12, 2023• 6 citations
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Abstract

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of $\mathrm{SU}(N)$ Hubbard models at any integer filling $\ensuremath{\rho}$. By calculating the ground states of one-dimensional $\mathrm{SU}(N)$ Fermi-Hubbard models for $2\ensuremath{\le}N\ensuremath{\le}6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U\ensuremath{\gg}t$, where $U$ and $t$ denote the on-site interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately ${(t/U)}^{2}$ for $\ensuremath{\rho}=1$ at intermediate and large lattice sizes on the basis of numeric and semianalytic arguments.

DOI
10.1103/physreva.107.043313

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We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the noise correlations contain full information on the most important fluctuations present in the system. We point out the importance of the sum rules fulfilled by the noise correlations and show that they yield nonsingular structures beyond the predictions of bosonization approaches. Noise correlations can thus serve as a universal probe of order and can be used to characterize the many-body states of cold atoms in optical lattices.
We investigate the dynamics of correlation propagation in the one-dimensional Fermi-Hubbard model with SU(NNN) symmetry when the repulsive-interaction strength is quenched from a large value, at which the ground state is a Mott-insulator with 1/N1/N1/N filling, to an intermediate value. From approximate analytical insights based on a simple model that captures the essential physics of the doublon excitations, we show that entanglement in the initial state leads to collective enhancement of the propagation velocity vSU(N)v_{\text{SU}(N)}vSU(N)​ when N>2N>2N>2, becoming equal to the velocity of the Bose-Hubbard model in the large-NNN limit. These results are supported by numerical calculations of the density-density correlation in the quench dynamics for N=2,3,4,N=2,3,4,N=2,3,4, and 666.
We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band filling using the dynamical density-matrix renormalization-group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic x-ray scattering, neutron scattering, and angle-resolved photoemission spectroscopy in the quasi-one-dimensional Mott insulator SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
The one-dimensional SU(n)\mathrm{SU}(n)SU(n) Hubbard model is investigated numerically for n=2n=2n=2, 3, 4, and 5 at half-filling and 1∕n1∕n1∕n filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive UUU if n>2n>2n>2. Furthermore, it is shown that the transition to the gapped phase at Uc=0{U}_{c}=0Uc​=0 is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd nnn. In the 1∕n1∕n1∕n-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for U>Uc=0U>{U}_{c}=0U>Uc​=0, the spin sector remains gapless, and the ground state is nondimerized.
More is uncorrelated: Tuning the local correlations of SU(NNN) Fermi-Hubbard systems via controlled symmetry breaking
Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number NNN of components. The value of NNN can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU(NNN) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the \emph{inter-flavor mutual information}, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing NNN further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for N=4N=4N=4 and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases -- a metal, a band insulator, and a Mott insulator -- all coexisting at a single tricritical point.
We study the properties of the ground states of the one- and two-dimensional Hubbard models at half-filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix renormalization group (DMRG). In particular, we investigate quantities such as the single-site entropy and two-site mutual information of single-particle momentum states as well as the behavior of the bipartite subsystem entropy for partitions in momentum space. The distribution of these quantities in momentum space gives insight into the fundamental nature of the ground state, insight that can be used to make contact with weak-coupling-based analytic approaches and to optimize numerical methods, the momentum-space DMRG in particular. We study the site and subsystem entropies as a function of interaction strength UUU and system size. In both the one- and two-dimensional cases, we find that the subsystem entropy scales proportionally to U2{U}^{2}U2 for weak UUU and proportionally to volume. Nevertheless, the optimized momentum-space DMRG can provide variationally accurate results for the two-dimensional Hubbard model at weak coupling for moderate system sizes.