The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum Gibbs states, which are quantum statistical equilibria with prescribed particle, current, and energy densities at each point of space (here R d , d $\ge$ 1). They assume that such local Gibbs states exist, and show that if the quantum system is initially in a local Gibbs state, then the system stays, in an appropriate asymptotic limit, in a Gibbs state with particle, current, and energy densities now solutions to the Euler equations. Our main contribution in this work is to prove that such local quantum Gibbs states can be constructed from prescribed densities under mild hypotheses, in both the fermionic and bosonic cases. The problem consists in minimizing the von Neumann entropy in the quantum grand canonical picture under constraints of local particle, current, and energy densities. The main mathematical difficulty is the lack of compactness of the minimizing sequences to pass to the limit in the constraints. The issue is solved by defining auxiliary constrained optimization problems, and by using some monotonicity properties of equilibrium entropies.The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum Gibbs states, which are quantum statistical equilibria with prescribed particle, current, and energy densities at each point of space (here R d , d $\ge$ 1). They assume that such local Gibbs states exist, and show that if the quantum system is initially in a local Gibbs state, then the system stays, in an appropriate asymptotic limit, in a Gibbs state with particle, current, and energy densities now solutions to the Euler equations. Our main contribution in this work is to prove that such local quantum Gibbs states can be constructed from prescribed densities under mild hypotheses, in both the fermionic and bosonic cases. The problem consists in minimizing the von Neumann entropy in the quantum grand canonical picture under constraints of local particle, current, and energy densities. The main mathematical difficulty is the lack of compactness of the minimizing sequences to pass to the limit in the constraints. The issue is solved by defining auxiliary constrained optimization problems, and by using some monotonicity properties of equilibrium entropies.

arXiv:2103.07310Mar 12, 20210 citations

Dynamical entropy for quantum systems

Göran Lindblad

Lecture notes in mathematicsJan 1, 19889 citations

Symmetry-enforced minimal entanglement and correlation in quantum spin chains

Kangle Li, Liujun Zou

The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the SO(3) S O ( 3 ) spin rotation symmetry and lattice translation symmetry in a quantum spin- J J chain, with J J a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi- \alpha α entropy compatible with these symmetries is \min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \} min { − 2 α − 1 ln ( 1 2 α ( 1 + 1 ( 2 J + 1 ) α − 1 ) ) , 2 ln ( J + 1 ) } , for any \alpha∈\mathbb{R}^+ α ∈ ℝ + . In an infinitely long open chain with such symmetries, for any \alpha∈\mathbb{R}^+ α ∈ ℝ + the minimal Rényi- \alpha α entropy of half of the system is \min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \} min { − 1 α − 1 ln ( 1 2 α ( 1 + 1The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the SO(3) S O ( 3 ) spin rotation symmetry and lattice translation symmetry in a quantum spin- J J chain, with J J a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi- \alpha α entropy compatible with these symmetries is \min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \} min { − 2 α − 1 ln ( 1 2 α ( 1 + 1 ( 2 J + 1 ) α − 1 ) ) , 2 ln ( J + 1 ) } , for any \alpha∈\mathbb{R}^+ α ∈ ℝ + . In an infinitely long open chain with such symmetries, for any \alpha∈\mathbb{R}^+ α ∈ ℝ + the minimal Rényi- \alpha α entropy of half of the system is \min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \} min { − 1 α − 1 ln ( 1 2 α ( 1 + 1

arXiv:2412.20765SciPost PhysicsJul 17, 20250 citations

Universal Algebraic Growth of Entanglement Entropy in Many-Body Localized Systems with Power-Law Interactions

Xiaolong Deng, Guido Masella, Guido Pupillo +1 more

Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, S_{vN}(t)∝t^{γ}. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent γ acquires a universal value γ_{c}≃0.33 at the many-body localization transition, for different lattice models, decay powers, filling factors, or initial conditions. Moreover, our results suggest an intriguing relation between γ_{c} and the critical minimal decay power of interactions necessary for many-body localization.Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, S_{vN}(t)∝t^{γ}. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent γ acquires a universal value γ_{c}≃0.33 at the many-body localization transition, for different lattice models, decay powers, filling factors, or initial conditions. Moreover, our results suggest an intriguing relation between γ_{c} and the critical minimal decay power of interactions necessary for many-body localization.

arXiv:1912.08131Physical Review LettersJun 29, 202038 citations

Maximum entropy principle for many-body ground states

N. Canosa, R. Rossignoli, Angelo Plastino

Nuclear Physics AApr 1, 199034 citations

\ge

1). They assume that such local Gibbs states exist, and show that if the quantum system is initially in a local Gibbs state, then the system stays, in an appropriate asymptotic limit, in a Gibbs state with particle, current, and energy densities now solutions to the Euler equations. Our main contribution in this work is to prove that such local quantum Gibbs states can be constructed from prescribed densities under mild hypotheses, in both the fermionic and bosonic cases. The problem consists in minimizing the von Neumann entropy in the quantum grand canonical picture under constraints of local particle, current, and energy densities. The main mathematical difficulty is the lack of compactness of the minimizing sequences to pass to the limit in the constraints. The issue is solved by defining auxiliary constrained optimization problems, and by using some monotonicity properties of equilibrium entropies.