Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

Piroli, Lorenzo; Calabrese, Pasquale

doi:10.1088/1751-8113/47/38/385003

Cited by 41 publications

(55 citation statements)

References 106 publications

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“…Finally, e[ρ] is the energy density defined in Eq. (34). The functional integral (94) can now be computed by saddle-point evaluation, leading to the condition…”

Section: The Quench Action Methodsmentioning

confidence: 99%

Integrable quenches in nested spin chains I: the exact steady states

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

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101

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We consider quantum quenches in the integrable SU (3)-invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable "soliton non-preserving" boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a Quantum Transfer Matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the Quench Action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states. arXiv:1811.00432v4 [cond-mat.stat-mech]

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“…Finally, e[ρ] is the energy density defined in Eq. (34). The functional integral (94) can now be computed by saddle-point evaluation, leading to the condition…”

Section: The Quench Action Methodsmentioning

confidence: 99%

Integrable quenches in nested spin chains I: the exact steady states

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

Self Cite

101

View full text Add to dashboard Cite

show abstract

“…The key ingredients are the overlaps between the initial state and all the eigenstates of the post-quench Hamiltonian, although a subset of the thermodynamically relevant overlaps may be sufficient (see [107][108][109]). Crucially, for a large class of initial states the overlaps can be calculated analytically [102,[110][111][112][113][114][115][116][117][118][119][120][121][122][123][124]. Overlap calculations are possible also for systems in the continuum, such as the Lieb-Liniger gas.…”

Section: Tba Approach For the Stationary Rényi Entropiesmentioning

confidence: 99%

Rényi entropies of generic thermodynamic macrostates in integrable systems

Mestyán¹,

Alba²,

Calabrese³

2018

J. Stat. Mech.

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We study the behaviour of Rényi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the Rényi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary Rényi entropies after the quench from the dimer and the tilted Néel state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full details the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies.

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“…However, the calculation of measurable observables is limited by the (un-)knowledge of the form factors even for the quench dynamics. Furthermore, the knowledge of more general form factors greatly helps also in the determination of exact formulas for the overlaps between initial state and Bethe states in the quench dynamics which nowadays are known only in very few cases [35,27,39,40,41,42,43].…”

Section: Introductionmentioning

confidence: 99%

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Piroli¹,

Calabrese²

2015

J. Phys. A: Math. Theor.

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Abstract. We present exact formulas for the form factors of local operators in the repulsive Lieb-Liniger model at finite size. These are essential ingredients for both numerical and analytical calculations. From the theory of Algebraic Bethe Ansatz, it is known that the form factors of local operators satisfy a particular type of recursive relations. We show that in some cases these relations can be used directly to derive practical expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size. Our main results are determinant formulas for the form factors of the operators (Ψ † (0)) 2 Ψ 2 (0) and Ψ R (0), for arbitrary integer R, where Ψ, Ψ † are the usual field operators. From these expressions, we also derive the infinite size limit of the form factors of these local operators in the attractive regime.

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Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

Cited by 41 publications

References 106 publications

Integrable quenches in nested spin chains I: the exact steady states

Integrable quenches in nested spin chains I: the exact steady states

Rényi entropies of generic thermodynamic macrostates in integrable systems

Exact formulas for the form factors of local operators in the Lieb–Liniger model

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