Abstract The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation. We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species. Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. Finally, Considering variations in the interaction between pairs of fermions λ FF , pairs of bosons λ BB , and variations in the interaction between particles of different species λ BF , we calculated the fidelity in the λ FF − λ BF and λ BB − λ BF planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.Abstract The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation. We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species. Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. Finally, Considering variations in the interaction between pairs of fermions λ FF , pairs of bosons λ BB , and variations in the interaction between particles of different species λ BF , we calculated the fidelity in the λ FF − λ BF and λ BB − λ BF planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.

Physica ScriptaMay 3, 20241 citation

On the Relation between Fermions and Bosons

Morikazu Toda

Journal of the Physical Society of JapanMar 1, 19526 citations

A generalization of the one-dimensional boson–fermion duality through the path-integral formalism

Satoshi Ohya

We study boson–fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson–fermion duality between the Lieb–Liniger model and the Cheon–Shigehara model. We present an explicit construction of n-boson and n-fermion models which are dual to each other and characterized by n−1 distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson–fermion mapping, and the strong–weak duality. We also discuss a scale-invariant generalization of the boson–fermion duality.We study boson–fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson–fermion duality between the Lieb–Liniger model and the Cheon–Shigehara model. We present an explicit construction of n-boson and n-fermion models which are dual to each other and characterized by n−1 distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson–fermion mapping, and the strong–weak duality. We also discuss a scale-invariant generalization of the boson–fermion duality.

arXiv:2105.04288Annals of PhysicsOct 26, 202112 citations

How bosonic is a pair of fermions?

Malte C. Tichy, Peter Alexander Bouvrie, Klaus Mølmer

arXiv:1310.8488Applied Physics BJun 4, 201416 citations

Exact lattice bosonization of the double-scaled $c=1$ matrix modelExact lattice bosonization of the double-scaled $c=1$ matrix model

Adwait Gaikwad, Gautam Mandal, Ajay Mohan

In a recent paper by two of us, it has been shown that entanglement entropy (EE) of matrix quantum mechanics (or, equivalently, of a non-relativistic fermion model) has a natural interpretation in terms of an exact bosonization of the fermion theory in terms of a lattice boson with lattice spacing $\sim 1/N$ (where $N$ is the rank of the matrix, equal to the number of fermions). The theory of this lattice boson is distinct from a latticized version of the "collective variable'' theory which is formulated in terms of the fermion density $ρ(λ)$ ("collective variable''); it is, in fact, more closely related to the Wigner distribution of the fermions. In this paper, we develop this connection further for the $c=1$ double scaled matrix model. Even though $N$ becomes infinite, the double scaled theory is described by a boson on a finite and non-uniform lattice spacing, of order $\sim g_s(x) l_s$ (where $g_s(x) \equiv g_s {\rm cosech}^2(x/l_s)$ is a position dependent string coupling). We explicitly derive the $c=1$ EE, as well as the one and two-point functions of fermion density from the lattice boson. The results are explicitly finite, unlike the collective variable theory which is shown to yield divergent answers. Our results suggest that while local observables such as the EE and $\langle ρ(λ) \rangle$ , are characterized by a unique short distance scale $g_s(x) l_s$ , the asymptotic observables such as the S-matrix at every genus are characterized by a short distance scale $l_s$ . We show how this arises and discuss a possible interpretation in terms of D0 brane physics.In a recent paper by two of us, it has been shown that entanglement entropy (EE) of matrix quantum mechanics (or, equivalently, of a non-relativistic fermion model) has a natural interpretation in terms of an exact bosonization of the fermion theory in terms of a lattice boson with lattice spacing $\sim 1/N$ (where $N$ is the rank of the matrix, equal to the number of fermions). The theory of this lattice boson is distinct from a latticized version of the "collective variable'' theory which is formulated in terms of the fermion density $ρ(λ)$ ("collective variable''); it is, in fact, more closely related to the Wigner distribution of the fermions. In this paper, we develop this connection further for the $c=1$ double scaled matrix model. Even though $N$ becomes infinite, the double scaled theory is described by a boson on a finite and non-uniform lattice spacing, of order $\sim g_s(x) l_s$ (where $g_s(x) \equiv g_s {\rm cosech}^2(x/l_s)$ is a position dependent string coupling). We explicitly derive the $c=1$ EE, as well as the one and two-point functions of fermion density from the lattice boson. The results are explicitly finite, unlike the collective variable theory which is shown to yield divergent answers. Our results suggest that while local observables such as the EE and $\langle ρ(λ) \rangle$, are characterized by a unique short distance scale $g_s(x) l_s$, the asymptotic observables such as the S-matrix at every genus are characterized by a short distance scale $l_s$. We show how this arises and discuss a possible interpretation in terms of D0 brane physics.

arXiv:2610.34376Oct 25, 20260 citations

Exact lattice bosonization of the double-scaled

c=1

matrix model

\sim 1/N

(where

N

is the rank of the matrix, equal to the number of fermions). The theory of this lattice boson is distinct from a latticized version of the "collective variable'' theory which is formulated in terms of the fermion density

ρ(λ)

("collective variable''); it is, in fact, more closely related to the Wigner distribution of the fermions. In this paper, we develop this connection further for the

c=1

double scaled matrix model. Even though

N

becomes infinite, the double scaled theory is described by a boson on a finite and non-uniform lattice spacing, of order

\sim g_s(x) l_s

(where

g_s(x) \equiv g_s {\rm cosech}^2(x/l_s)

is a position dependent string coupling). We explicitly derive the

c=1

EE, as well as the one and two-point functions of fermion density from the lattice boson. The results are explicitly finite, unlike the collective variable theory which is shown to yield divergent answers. Our results suggest that while local observables such as the EE and

\langle ρ(λ) \rangle

, are characterized by a unique short distance scale

g_s(x) l_s

, the asymptotic observables such as the S-matrix at every genus are characterized by a short distance scale

l_s

. We show how this arises and discuss a possible interpretation in terms of D0 brane physics.