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Quantum quenches in the anisotropic spin-½ Heisenberg chain: different approaches to many-body dynamics far from equilibrium.

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Title: Quantum quenches in the anisotropic spin-½ Heisenberg chain: different approaches to many-body dynamics far from equilibrium.
Authors: Barmettler, Peter1,2 peter.barmettler@cpht.polytechnique.fr, Punk, Matthias2, Gritsev, Vladimir1, Demler, Eugene3, Altman, Ehud4
Source: New Journal of Physics. May2010, Vol. 12 Issue 5, p1-50. 50p. 14 Graphs.
Subjects: Heisenberg uncertainty principle, Spin waves, Many-body problem, Anisotropy, Ultracold neutrons, Quantum theory
Abstract: Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian. [ABSTRACT FROM AUTHOR]
Copyright of New Journal of Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: <searchLink fieldCode="JN" term="%22New+Journal+of+Physics%22">New Journal of Physics</searchLink>. May2010, Vol. 12 Issue 5, p1-50. 50p. 14 Graphs.
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  Data: <searchLink fieldCode="DE" term="%22Heisenberg+uncertainty+principle%22">Heisenberg uncertainty principle</searchLink><br /><searchLink fieldCode="DE" term="%22Spin+waves%22">Spin waves</searchLink><br /><searchLink fieldCode="DE" term="%22Many-body+problem%22">Many-body problem</searchLink><br /><searchLink fieldCode="DE" term="%22Anisotropy%22">Anisotropy</searchLink><br /><searchLink fieldCode="DE" term="%22Ultracold+neutrons%22">Ultracold neutrons</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink>
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  Data: Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of New Journal of Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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