Relaxation in the<i>XX</i>quantum chain

Platini, Thierry; Karevski, Dragi

doi:10.1088/1751-8113/40/8/002

Cited by 70 publications

(81 citation statements)

References 29 publications

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“…2 for various values of the interaction parameter ∆. The Fermi velocity (shown on the left) is found to be very well approximated by the square root expression (24) reported in the main text, although deviations increase with increasing |∆|. Finally, the expectation value on the upper half plane is simply given by…”

Section: Discussionmentioning

confidence: 63%

“…when two parts of a system are prepared initially in their (otherwise homogeneous) ground states with different magnetizations. The resulting front structures have been widely studied for the XX [22][23][24][25][26][27][28][29], the transverse Ising [30][31][32][33][34] and the XXZ chains [11,27,31,35,36]. In the latter case, a remarkable analytical solution has been found very recently [37], using the method of generalized hydrodynamics (GHD).…”

Section: Introductionmentioning

confidence: 99%

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Front dynamics and entanglement in the XXZ chain with a gradient

Eisler

Bauernfeind

2017

Phys. Rev. B

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We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

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Section: Discussionmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Front dynamics and entanglement in the XXZ chain with a gradient

Eisler

Bauernfeind

2017

Phys. Rev. B

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“…Quantum quench protocols have received these recent years much attention as for example in the context of the quantum version of fluctuation theorem [28], the relaxation properties toward a local canonical ensemble or a generalized version of Gibbs ensemble depending on the integrability of the system, see [27] for a review. Many of these investigations focused not only on steady properties but also on dynamical aspects like front propagation of an initial density inhomogeneity [29][30][31][32] or the expansion of a cloud of particles after the more or less sudden release of a trap [33][34][35][36]. Our main goal here is to investigate how the quench, that is how the relaxation of the environment toward a local steady state [27], influences, with respect to the equilibrium case treated in [25], the disentanglement of the two distant qubits initially prepared in a Bell state.…”

Section: Introductionmentioning

confidence: 99%

Decoherence of Bell states by local interactions with a suddenly quenched spin environment

2014

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We study the dynamics of disentanglement of two qubits initially prepared in a Bell state and coupled at different sites to an Ising transverse field spin chain (ITF) playing the role of a dynamic spin environment. The initial state of the whole system is prepared into a tensor product state ρ Bell ⊗ ρ chain where the state of the chain is taken to be given by the ground state |G(λi) of the ITF Hamiltonian HE(λi) with an initial field λi. At time t = 0 + , the strength of the transverse field is suddenly quenched to a new value λ f and the whole system (chain + qubits) undergoes a unitary dynamics generated by the total Hamiltonian HT ot = HE(λ f ) + HI where HI describes a local interaction between the qubits and the spin chain. The resulting dynamics leads to a disentanglement of the qubits, which is described through the Wooter's Concurrence, due to there interaction with the non-equilibrium environment. The concurrence is related to the Loschmidt echo which in turn is expressed in terms of the time-dependent covariance matrix associated to the ITF. This permits a precise numerical and analytical analysis of the disentanglement dynamics of the qubits as a function of their distance, bath properties and quench amplitude. In particular we emphasize the special role played by a critical initial environment.

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“…At the moment, we do not see why this condition should matter. A definite answer can be given working out the exact solution (7). That is a cumbersome calculation that we leave to future works.…”

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confidence: 99%

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

2017

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We derive a Moyal dynamical equation that describes exact time evolution in generic (inhomogeneous) noninteracting spin-chain models. Assuming quasistationarity, we develop a hydrodynamic theory. The question at hand is whether some large-time corrections are captured by higher-order hydrodynamics. We consider in particular the dynamics after that two chains, prepared in different conditions, are joined together. In these situations a light cone, separating regions with macroscopically different properties, emerges from the junction. In free fermionic systems some observables close to the light cone follow a universal behavior, known as Tracy-Widom scaling. Universality means weak dependence on the system's details, so this is the perfect setting where hydrodynamics could emerge. For the transverse-field Ising chain and the XX model, we show that hydrodynamics captures the scaling behavior close to the light cone. On the other hand, our numerical analysis suggests that hydrodynamics fails in more general models, whenever a condition is not satisfied.Over the past few years, we are experiencing an increasing interest in the physics behind the nonequilibrium time evolution of inhomogeneous states. An example is the time evolution of two semi-infinite chains that are joined together after having been prepared in different equilibrium conditions [1,2]. This kind of settings allows one to investigate the transport properties of quantum many-body systems even if the system is isolated from the environment.The first analytic results in this context were obtained in noninteracting models . There, under the assumption of quasistationarity, a semiclassical picture applies where the information about the initial state is carried by free stable quasiparticles moving throughout the system. Similar results were obtained in the framework of conformal field theory and Luttinger liquid descriptions [25][26][27][28][29][30][31][32][33][34][35][36][37]. In the presence of interactions the situation was less clear [38][39][40][41][42][43][44][45][46][47], but, eventually, Refs [48,49] have shown that the continuity equations satisfied by the (quasi)local conserved quantities are sufficient to characterize the late-time behavior. The framework developed in Refs [48,49] is now known as generalized hydrodynamics [48], where "generalized" is used to emphasize that integrable models have infinitely many (quasi)local charges [50]. We will generally omit "generalized" and refer to the system of equations derived in [48,49] as first-order hydrodynamics, 1 st GHD, to emphasize that it is a system of first-order partial differential equations.Within 1 st GHD, it was possible to compute the profiles of local observables [48,49,[51][52][53][54][55][56][57], to conjecture an expression for the time evolution of the entanglement entropy [58], and to efficiently calculate Drude weights [59][60][61][62][63]. There are however fundamental questions that can not be addressed within 1 st GHD; diffusive transport [64][65][66][67][68][69] and large-tim...

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Relaxation in theXXquantum chain

Cited by 70 publications

References 29 publications

Front dynamics and entanglement in the XXZ chain with a gradient

Front dynamics and entanglement in the XXZ chain with a gradient

Decoherence of Bell states by local interactions with a suddenly quenched spin environment

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

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