Full Counting Statistics in a Propagating Quantum Front and Random Matrix Spectra

Eisler, Viktor; Rácz, Zoltán

doi:10.1103/physrevlett.110.060602

Cited by 160 publications

(248 citation statements)

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“…The symbols are exact numerical data (in a chain with 1801 spins) at three different times t = 60, 150, 380, after that a thermal state with inverse temperature β = 1 has been put in contact with the infinite-temperature state. The lines are the predictions (20). The agreement is fair, but the data do not seem to approach the predictions as the time is increased.…”

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confidence: 60%

“…There are however fundamental questions that can not be addressed within 1 st GHD; diffusive transport [64][65][66][67][68][69] and large-time corrections [20][21][22][23] are two of them. The importance of these issues results in a considerable urge to fill these gaps [61], passing through refinements and reinterpretations of the theory [57,[70][71][72][73].…”

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confidence: 99%

“…It could be effective, however, for corrections exhibiting universal properties, like the ones studied in Ref. [20]. There, the time evolution of a domain-wall state under a free fermionic Hamiltonian (XX model) was considered.…”

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confidence: 99%

“…Following Ref. [20], we consider the scaling limit where the time is large and both r − v(p)t and the subsystem's length |S| are proportional to t 1 3 . Assuming the various functions to be sufficiently smooth around p =p we find…”

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

Fagotti

2017

Phys. Rev. B

122

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

Fagotti

2017

Phys. Rev. B

122

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“…Under time evolution the initial inhomogeneity spreads ballistically, creating a front region which grows linearly in time. While the overall shape of the front is simple to obtain from a hydrodynamic (semiclassical) picture in terms of the fermionic excitations [9], the fine structure is more involved and shows universal features around the edge of the front [10,11] The melting of domain walls has been considered in various different lattice models, such as the transverse Ising [12,13], the XY [14] and XXZ chains [15][16][17][18], hard-core bosons [19][20][21], as well as in the continuum for a Luttinger model [22], the Lieb-Liniger gas [23] or within conformal field theory [24,25]. Instead of a sharp domain wall, the melting of inhomogeneous interfaces can also be studied by applying a magnetic field gradient, which is then suddenly quenched to zero [26][27][28].…”

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confidence: 99%

Universal front propagation in the quantum Ising chain with domain-wall initial states

2016

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We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

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Domain Walls in the Heisenberg-Ising Spin- $$\frac {1}{2}$$ Chain

Saenz

Tracy²,

Widom³

2022

Toeplitz Operators and Random Matrices

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Full Counting Statistics in a Propagating Quantum Front and Random Matrix Spectra

Cited by 160 publications

References 32 publications

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

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

Universal front propagation in the quantum Ising chain with domain-wall initial states

Domain Walls in the Heisenberg-Ising Spin- $$\frac {1}{2}$$ Chain

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