2011/01/31 by Ayoti Patra, Victor Mukherjee, Amit Dutta
Mathematics · Physics and Astronomy · #Anisotropy #Condensed matter physics #Critical dimension #Critical exponent #Critical phenomena #Critical point (mathematics) #Exponent #Mathematical analysis #Mathematics #Phase (matter) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Spins #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1088/1742-5468/2011/03/p03026
published as J. Stat. Mech. (2011) P03026 · 5 pages, 6 figures
openalex publication_date 2011/03/28 · arxiv created 2011/03/30 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 = α c = 2. For α > α c , or on the paramagnetic side, no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.