Quench dynamics of the anisotropic heisenberg model

Physical Review Letters

Volumn 112, Issue 25, 2014, Pages

  Liu, Wenshuo ^a   Andrei, Natan ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; PHYSICS;

ANALYTICAL APPROACH; ANISOTROPIC HEISENBERG MODELS; ANTIFERROMAGNETIC ORDERINGS; CONTOUR REPRESENTATION; INTEGRAL FORM; LOCAL MAGNETIZATION; TIME EVOLUTIONS; TIME-DEPENDENT WAVE FUNCTION;

ANISOTROPY;

EID: 84903531328     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.257204     Document Type: Article

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26. The argument in Refs. [22-25], which proceeds via contours that avoid pole contributions, cannot be applied here. Instead, the proof proceeds via a delicate cancellation of residues [27].
27. W. Liu and N. Andrei (to be published).
28. For example, in Ref. [21], the coupling (Equation presented). Thus, the dimensionless time unit (Equation presented) in our convention corresponds to (Equation presented) ms in their experiment. See Fig. 2 for details of this comparison.
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32. The Heaviside step function (Equation presented) is defined as (Equation presented) when (Equation presented), (Equation presented) when (Equation presented). The definition of (Equation presented) is not necessary here, since (Equation presented).
33. In the region (Equation presented), one moves the back-running contours to (Equation presented) instead of (Equation presented), so the order of strings generated is restricted by the value of the anisotropy (Equation presented). This feature agrees with the traditional thermodynamic Bethe ansatz.
34. For the region (Equation presented), there is actually another term (Equation presented). But it is trivial, since the integral without an (Equation presented)-matrix can be decoupled for each (Equation presented).
35. According to the dispersion relation of an (Equation presented)-string [31], the maximum velocities are given by (Equation presented), (Equation presented).
36. According to the dispersion relation of an (Equation presented)-string [31], the maximum velocities are given by (Equation presented), (Equation presented).