Fermions with long-range interactions using a matrix-product-states approach

Roberto Bondesan, Thomas Quella

Jheng-Wei Li, Xavier Waintal

Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence matrix product state (MPS) methods based on moderate entanglement have been overwhelmingly formulated in the second quantization. Here we introduce a first-quantized MPS approach to simulate quantum many-body systems. We show that, by reformulating the way the fermionic antisymmetry is handled, we arrive at MPS with a level of entanglement comparable to the usual one found in the second quantization. We demonstrate our scheme on the one-dimensional t-V model (spinless fermions with density-density interaction) for both ground state and time evolution. For the ground state, we find that the first quantization approach naturally extends to long-range interaction in the Wigner crystal regime. For time evolution, we find that the entanglement entropy in first quantization is significantly smaller than in its second quantization counterpart.

Pirmin Lemberger, Nicolas Macris

Alan Coleman

Bradraj Pandey, Elbio R. Dagotto, Swapan Kumar Pati

Motivated by recent experiments in fermionic polar gases, we study the nonequilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian by calculating experimentally accessible dynamical observables. To study the nonequilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons $|\ensuremath{\uparrow}\ensuremath{\downarrow}0\ensuremath{\uparrow}\ensuremath{\downarrow}0\ensuremath{\uparrow}\ensuremath{\downarrow}0\ensuremath{\uparrow}\ensuremath{\downarrow}0\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\rangle}$ and (ii) product state with singlons $|\ensuremath{\uparrow}\ensuremath{\downarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\downarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\downarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\downarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\downarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\rangle}$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization (ED) and the time-dependent variational principle (TDVP) for finite matrix product states (MPS), within experimentally relevant timescales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. In addition to the quench dynamics, we also demonstrate the localization of charge and spin in the full energy spectrum of the long-range spin-SU(2) symmetric Hamiltonian by monitoring spin and charge autocorrelation functions. Our predictions for localization of both charge and spin should be observable in ultracold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.

I. V. Lukin, Andrii Sotnikov

We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly solvable Calogero-Moser model. We show the high accuracy of reproducing the ground-state properties of the many-body system and discuss potential errors that can originate from the approximation of the nonlocal interaction potentials with singularities.