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Register a new userOperationally accessible entanglement of one dimensional spinless fermions
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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 phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.
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We investigate the scaling of the R{e}nyi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second R{e}nyi entanglement entropy and show that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional $t-V$ model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.
We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling $2/3$.
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to quantum simulation and quantum computation due to their computational complexity. In this article, we exploit spectral graph theory to completely characterize the symmetry properties of one-dimensional fermionic mixtures in the strong interaction limit. We also develop a powerful method to obtain the so-called Tan contacts associated with certain symmetry classes. In particular, compared to brute force diagonalization that is already virtually impossible for a moderate number of fermions, our analysis enables us to make unprecedented efficient predictions about the energy gap of complex spin mixtures. Our theoretical results are not only of direct experimental interest, but also provide important guidance for the design of adiabatic control protocols in strongly correlated fermion mixtures.
The time dependent quantum Monte Carlo method for fermions is introduced and applied for calculation of entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by the method allows one to build reduced density matrices for each electron and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small and it is determined mostly by the quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case the outermost opposite-spin electrons interact like bosons which prevails their entanglement, while the inner shell electrons remain largely at their Hartree-Fock geometry. Our findings are in a close correspondence with the numerically exact results, wherever such comparison is possible.
We consider a system of one-dimensional fermions moving in one direction, such as electrons at the edge of a quantum Hall system. At sufficiently long time scales the system is brought to equilibrium by weak interactions between the particles, which conserve their total number, energy, and momentum. Time evolution of the system near equilibrium is described by hydrodynamics based on the three conservation laws. We find that the system supports three sound modes. In the low temperature limit one mode is a pure oscillation of particle density, analogous to the ordinary sound. The other two modes involve oscillations of both particle and entropy densities. In the presence of disorder, the first sound mode is strongly damped at frequencies below the momentum relaxation rate, whereas the other two modes remain weakly damped.
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