Separation of Time Scales in a Quantum Newton’s Cradle

Berg, R. van den; Wouters, Bram; Eliens, Sebas; Nardis, Jacopo De; Konik, Robert; Caux, Jean-Sébastien

doi:10.1103/physrevlett.116.225302

Cited by 45 publications

(65 citation statements)

References 56 publications

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“…The finite temperature partition function of the XY model for h < 1 is 33) where the terms with a minus sign within each square bracket kill states with the wrong parity of excitations in each sector. Taking the thermodynamic limit, the free energy per site is: 34) where the last term, encoding the degeneracy of the model, is clearly negligible in the thermodynamic limit.…”

Section: The Phase-diagrammentioning

confidence: 99%

“…Taking the logarithm we get 33) where theĨ j are a set of integers which define the state. In the second line we introduced a new set I j : they are integers if the number of particles N is odd and half-integers if N is even 3 .…”

Section: The Bethe Equationsmentioning

confidence: 99%

“…The main limitation in the physical application of the model is that the Bethe Ansatz solution assumes translational invariance, which is spoiled by the trapping used in current cold atoms experimental implementations. In fact, due to the external potential, real systems are inhomogeneous, with a density of particles that varies in space [31,32,33]. While introducing an external potential in (2.1) spoils integrability, we should mention that there is a different kind of potential that admits a parabolic confinement and is also exactly solvable, namely the Calogero-Moser model [34]:…”

Section: Introductionmentioning

confidence: 99%

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An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Franchini

2017

Lecture Notes in Physics

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Section: The Phase-diagrammentioning

confidence: 99%

Section: The Bethe Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Franchini

2017

Lecture Notes in Physics

197

235

View full text Add to dashboard Cite

“…In particular, while an impressive number of results have been derived in theories that can be mapped onto free fermionic systems (see Ref. [14] for a comprehensive review), only a few special cases exist where analytic computations could be done in the presence of genuine interactions [18][19][20][21][22][23][24][25][26][27][28][29] . Furthermore, integrable models are by their own nature very special, and can not be representative of generic systems, which are expected to display qualitatively different features.…”

Section: Introductionmentioning

confidence: 99%

Exact dynamics in dual-unitary quantum circuits

et al. 2020

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We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of "solvable" matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size reaches infinite temperature after a time t ∝ , irrespective of the presence of conserved quantities, the light-cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of non-solvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

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“…The bottleneck in this procedure occurs in the calculation of the overlaps which proves to be rather difficult. Outside of the Tonks-Girardeau (TG) limit of c → ∞, where calculations are simplified [34][35][36][37][38][39] , exact overlaps are scarce 40,41 . To simplify the calculation we shall use an alternate resolution of the identity that is particularly convenient when working with initial states like (4) which are ordered in real space 42 ,…”

Section: An Alternate Identitymentioning

confidence: 99%

Quantum work of an optical lattice

Rylands

Andrei

2019

Phys. Rev. B

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A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench. arXiv:1904.07995v2 [cond-mat.str-el]

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Separation of Time Scales in a Quantum Newton’s Cradle

Cited by 45 publications

References 56 publications

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Exact dynamics in dual-unitary quantum circuits

Quantum work of an optical lattice

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