Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Thakurathi, Manisha and Sen, Diptiman and Dutta, Amit (2012) Fidelity susceptibility of one-dimensional models with twisted boundary conditions. In: PHYSICAL REVIEW B, 86 (24).

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Abstract

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

Item Type:	Journal Article
Publication:	PHYSICAL REVIEW B
Publisher:	AMER PHYSICAL SOC
Additional Information:	Copyright for this article belongs to AMER PHYSICAL SOC, USA
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	28 Jan 2013 11:40
Last Modified:	28 Jan 2013 11:40
URI:	http://eprints.iisc.ac.in/id/eprint/45662

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