We analytically study a system of spinless fermions driven at the boundary with an oscillating chemical potential. Various transport regimes can be observed: at zero driving frequency the particle current through the system is independent of the system's length; at the phase-transition frequency, being equal to the bandwidth, the current decays as n^{-alpha} with the chain length n, alpha being either 2 or 3; below the transition the scaling of the current is n^{-1/2}, indicating anomalous transport, while it is exponentially small exp{(-n/2xi)} above the transition. Therefore, by a simple change of frequency of the a.c. driving one can vary transport from ballistic, anomalous, to insulating.
Flatiron Institute（弗莱提伦研究所）；New York University（纽约大学）
First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow inspired ansatz which exploits deep residual networks with convolutional residual blocks, we approximately determine the ground state of spinless fermions on a square lattice with nearest-neighbor interactions. The flexibility of the neural-network ansatz results in a high level of accuracy when compared to exact diagonalization results on small systems, both for energy and correlation functions. On large systems, we obtain accurate estimates of t…
We construct a 1D model Hamiltonian of spinless fermions for which the spinless analogue of $η$-pairing states are quantum many-body scars of the model. These states are excited states and display subvolume entanglement entropy scaling; they form a tower of states that are equally spaced in energy (resulting in periodic oscillations in the Loschmidt echo and in the time evolution of observables for initial states prepared in a superposition of them) and are atypical in the sense that they weakly break the eigenstate thermalization hypothesis, while the other excited states are thermal. We exte…
We introduce a class of spinless fermion models that exhibit quantum many-body scars (QMBS) originating from kinetic constraints in the form of density-assisted hopping. The models can be defined on any lattice in any dimension and allow for spatially varying interactions. We construct a tower of exact eigenstates with finite energy density, and we demonstrate that these QMBS are responsible for the nonthermal nature of the system by studying the entanglement entropy and correlation functions. The quench dynamics from certain initial states is also investigated, and it is confirmed that the QM…
Motivated by the experiment [St-Jean {\it et al}., Nature Photon. {\bf 11}, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless $p$-orbital fermions with local interorbital hoppings and repulsive interactions between $p_x$ and $p_y$ bands in zigzag optical lattices. We show that spinless $p$-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state …
We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in an homogeneous p + ip superconducting (SC) phase at high or low electron densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above Tsc, generating a…
This work unravels an interesting property of a one-dimensional lattice model that describes a single itinerant spinless fermion (excitation) coupled to zero-dimensional (dispersionless) bosons through two different nonlocal-coupling mechanisms. Namely, below a critical value of the effective excitation-boson coupling strength the exact ground state of this model is the zero-quasimomentum Bloch state of a bare (i.e., completely undressed) excitation. It is demonstrated here how this last property of the lattice model under consideration can be exploited for a fast, deterministic preparation of…
Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over parti…
For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order …
This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. In this sequel, we extend our computations in two significant ways. The first is to a relativistic spin-$\frac{1}{2}$ fermion and the second concerns the interpretation of the physics. Whereas in a previous paper, we speculated on the possibility of observing such condensed matter systems in the astrophysics of extreme magnetic sources such as neutron stars, the physical systems in this study are more down-to-earth objects such as a $\mathsf{C}_…
We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model. The relevant local observables, however, do not transform well under this mapping and take very complicated expressions in terms of the spinless fermions. Here we show that for two classes of interesting observables the quench dynamics from product states in the occupation basis can be determined exactly in terms of correlations in the tight-binding model. In …
By extending local U(1) gauge symmetry to discontinuous case, we find that under one special discontinuous U(1) gauge transformation the symmetric and antisymmetric wave functions can transform into each other in one dimensional quantum mechanics. The free spinless fermionic system and bosonic system with $δ$-type vector gauge potential are proved to be equivalent. The relation also holds in higher space-time dimensions.
One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials can also be mapped onto dual interacting fermions. However, a systematic approach to one-dimensional statistical transmutation for arbitrary low-energy interactions in the spinless and spinful or multicomponent cases has remained elusive. I develop a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions…
