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arXiv:2407.15609 · Physical review. B./Physical review. B

Time evolution of the local density of states of strongly correlated fermions coupled to a nanoprobe

T. Blum, R. M. Noack, Salvatore R. Manmana

Published Jan 27, 2025• 2 citations
arXivHTMLPDF

Abstract

We study the time evolution of a one-dimensional system of strongly correlated electrons (a ``sample'') that is suddenly coupled to a smaller, initially empty system (a ``nanoprobe''), which can subsequently move along the system. Our purpose here is to study the role of interactions in this model system when it is far from equilibrium. We therefore take both the sample and the nanoprobe to be described by a Hubbard model with on-site repulsive interactions and nearest-neighbor hopping. We compute the behavior of the local particle density and the local density of states (LDOS) as a function of time using time-dependent matrix product states at quarter and at half filling, fillings at which the chain realizes a Luttinger liquid or a Mott insulator, respectively. This allows us to study in detail the oscillation of the particles between the sample and the nanoprobe. While, for noninteracting systems, the LDOS is time independent, in the presence of interactions, the backflow of electrons to the sample will lead to nontrivial dynamics in the LDOS. In particular, studying the time-dependent LDOS allows us to study how the Mott gap closes locally and how this melting of the Mott insulator propagates through the system in time after such a local perturbation---a behavior that we envisage can be investigated in future experiments on ultrashort time scales or on optical lattices using microscopy setups.

DOI
10.1103/physrevb.111.035152

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We study the time evolution of a one-dimensional system of strongly correlated electrons (a sample'') that is suddenly coupled to a smaller, initially empty system (a nanoprobe''), which can subsequently move along the system. Our purpose here is to study the role of interactions in this model system when it is far from equilibrium. We therefore take both the sample and the nanoprobe to be described by a Hubbard model with on-site repulsive interactions and nearest-neighbor hopping. We compute the behavior of the local particle density and the local density of states (LDOS) as a function of time using time-dependent matrix product states at quarter and at half filling, fillings at which the chain realizes a Luttinger liquid or a Mott insulator, respectively. This allows us to study in detail the oscillation of the particles between the sample and the nanoprobe. While, for noninteracting systems, the LDOS is time independent, in the presence of interactions, the backflow of electrons to the sample will lead to nontrivial dynamics in the LDOS. In particular, studying the time-dependent LDOS allows us to study how the Mott gap closes locally and how this melting of the Mott insulator propagates through the system in time after such a local perturbation---a behavior that we envisage can be investigated in future experiments on ultrashort time scales or on optical lattices using microscopy setups.
We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.
We investigate the collapse and revival of the initial state of a system of spinless fermions on a one‐dimensional lattice with nearest‐neighbor Coulomb repulsion V and nearest‐neighbor hopping t at half filling which we push out of equilibrium. Starting from a Luttinger liquid phase, we suddenly increase the interaction to a value associated with an insulating ground state. Using a variant of the time‐dependent density matrix renormalization group method (DMRG) that approximates the time‐evolution operator within a Krylov subspace, we calculate the full time evolution of quantities like the momentum distribution 〈nk〉 and the local density 〈ni〉. In the atomic limit, t = 0, the density and the density‐density correlation function are time‐independent, while 〈nk〉 changes with time, showing that in out‐of‐equilibrium situations density‐density correlations and one‐particle propagators are no longer connected by a single anomalous dimension as in the equilibrium case. Since in this limit the initial state is reobtained after Trevival = 2π/(V/t), the collapse and revival of the initial Luttinger liquid equilibrium state is discussed. Preliminary results providing insight into the behavior in the thermodynamic limit for various parameter values with finite hopping amplitude t ≠ 0 are presented.
We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion UUU and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude ttt. We identify three different phases as functions of the disorder amplitude WWW and Coulomb interaction strength U>0U>0U>0. When U<4tU<4tU<4t the system shows a metallic phase: (i) only when no disorder is present W=0W=0W=0 or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When U>4tU>4tU>4t the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered samples. Here we consider a notable paradigm of strongly correlated Fermi systems, the Mott phase of the Hubbard model, in a setup resembling ultracold-gases experiments. We study the three-dimensional expansion of a cloud into an optical lattice after removing the confining potential. We use time-dependent density-functional theory combined with dynamical mean-field theory, considering interactions below and above the Mott threshold, as well as disorder effects. At strong coupling, we observe multiple timescales in the melting of the Mott wedding-cake structure, as the Mott plateau persist orders of magnitude longer than the band insulating core. We also show that disorder destabilises the Mott plateau and that, compared to a clean setup, localisation can decrease, creating an interesting dynamic crossover during the expansion.
We calculate the nonequilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to noninteracting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density-matrix renormalization-group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and we relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.