Patra, Ayoti ; Mukherjee, Victor ; Dutta, Amit (2011) Path-dependent scaling of geometric phase near a quantum multi-critical point Journal of Statistical Mechanics: Theory and Experiment, 2011 (03). P03026. ISSN 1742-5468
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Official URL: http://doi.org/10.1088/1742-5468/2011/03/P03026
Related URL: http://dx.doi.org/10.1088/1742-5468/2011/03/P03026
Abstract
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about the z axis by an angle η. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, up to a critical value α = αc = 2. For α > αc, or on the paramagnetic side, no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
Item Type: | Article |
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Source: | Copyright of this article belongs to IOP Publishing. |
ID Code: | 117200 |
Deposited On: | 16 Apr 2021 04:39 |
Last Modified: | 16 Apr 2021 04:39 |
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