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Signatures of Quantum Phase Transitions via Quantum Information Theoretic Measures

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Quantum Quenching, Annealing and Computation

Part of the book series: Lecture Notes in Physics ((LNP,volume 802))

Abstract

Quantum phase transitions (QPTs) in many body systems occur at \(T = 0\) brought about by tuning a non-thermal parameter, e.g. pressure, chemical composition or external magnetic field [1, 2]. In a QPT, the ground state wave function undergoes qualitative changes at the transition point. The transition is driven by quantum fluctuations whereas ordinary phase transitions occurring at nonzero temperatures are driven by thermal fluctuations. Like a thermal phase transition, a QPT can be first order, second order or higher order. The thermal critical point, associated with a second-order phase transition, is characterized by the presence of thermal fluctuations on all length scales resulting in a divergent correlation length. The free energy and the thermodynamic functions develop singularities as temperature \(T\rightarrow T_{\textrm{c}}\), the critical temperature. At the quantum critical point (QCP), quantum fluctuations occur on all length scales leading to a divergent correlation length. The ground state and related physical quantities become non-analytic as the tuning parameter g tends to the critical value g c . The influence of QPTs extends into the finite T part of the phase diagram so that experimental detection of QPTs is possible.

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Acknowledgement

A. T. is supported by the Council of Scientific and Industrial Research, India, under Grant No. 9/15 (306)/ 2004-EMR-I.

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Authors and Affiliations

  1. Department of Physics, Bose Institute, 93/1, A.P.C. Road, Kolkata, 700009, India

    I. Bose & A. Tribedi

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  1. I. Bose
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  2. A. Tribedi
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Correspondence to I. Bose or A. Tribedi .

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Editors and Affiliations

  1. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Anjan Kumar Chandra

  2. Theoretical Physics (ICTP), Abdus Salam International Centre for, Strada Costiera 11, Trieste, 34014, Italy

    Arnab Das

  3. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Bikas K. Chakrabarti

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Bose, I., Tribedi, A. (2010). Signatures of Quantum Phase Transitions via Quantum Information Theoretic Measures. In: Chandra, A., Das, A., Chakrabarti, B. (eds) Quantum Quenching, Annealing and Computation. Lecture Notes in Physics, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11470-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-11470-0_8

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