Scaling of the fidelity susceptibility in a disordered quantum spin chain
Open accessAbstract
The phase diagram of a quantum $XY$ spin chain with Gaussian-distributed random anisotropies and transverse fields is investigated, with focus on the fidelity susceptibility, a recently introduced quantum information theoretical measure. Monitoring the finite-size scaling of the probability distribution of this quantity as well as its average and typical values, we detect a disorder-induced disappearance of criticality and the emergence of Griffiths phases in this model. It is found that the fidelity susceptibility is not self-averaging near the disorder-free quantum-critical lines. At the Ising critical point the fidelity susceptibility scales as a disorder-strength independent stretched exponential of the system size, in contrast with the quadratic scaling at the corresponding point in the disorder-free $XY$ chain. Along the line where the average anisotropy vanishes the fidelity susceptibility appears to scale extensively, whereas in the disorder-free case this point is quantum critical with quadratic finite-size scaling.
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In higher-dimensional lattices, states obeying the Area law may still be amenable to classical simulation using tensor networks, density functional theories, or quantum Monte Carlo.
“In higher-dimensional lattices, states which obey the socalled 'Area law' [97], where quantum correlations are smaller than in generic states, may still be amenable to a classical simulation using state-of-the-art techniques such as tensor networks [77, 81, 82, 198, 199], Density Functional Theories [86], or Quantum Monte Carlo [75].”
From Can one trust quantum simulators? (2012) · cites this paper as [198]
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NUMERICAL STUDIES OF FRUSTRATED QUANTUM PHASE TRANSITIONS IN TWO AND ONE DIMENSIONS
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- Authors
- Jacobson, N. T., Garnerone, S., Haas, S., & Zanardi, P.
- Affiliations
- University of Southern California (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2009-05-26
- Volume
- 79
- Issue
- 18
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1995733193
- Cited by
- 33
- References
- 24
- Citations by year
- 2025: 3 · 2024: 2 · 2023: 2 · 2022: 1 · 2019: 2 · 2018: 1 · 2016: 2 · 2015: 1 · 2014: 6 · 2012: 4
- FWCI
- 2.41
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- fidelity susceptibility, quantum spin chains, disordered quantum systems, quantum XY model, Griffiths phase, finite-size scaling, quantum criticality, self-averaging, transverse field, quantum information measures
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