AroundConnect

2014

A Gaudin-like determinant for overlaps of N\'eel and XXZ Bethe states

Brockmann, Michael, De Nardis, Jacopo, Wouters, Bram et al.

Understand

We derive a determinant expression for overlaps of Bethe states of the XXZ spin chain with the N{\'e}el state, the ground state of the system in the antiferromagnetic Ising limit.

  • Our formula, of determinant form, is valid for generic system size.
  • Interestingly, it is remarkably similar to the well-known Gaudin formula for the norm of Bethe states, and to another recently-derived overlap formula appearing in the Lieb-Liniger model.

Built on

  • H. Bethe, Z. Phys. 71

    1931

    Earlier work this paper cites.

  • R. Orbach, Phys. Rev. 112

    1958

    Earlier work this paper cites.

  • E. H. Lieb and W. Liniger, Phys. Rev. 130

    1963

    Earlier work this paper cites.

  • E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, Theor. Math. Phys. 40

    1979

    Earlier work this paper cites.

  • M. Gaudin, B. M. McCoy, and T. T. Wu, Phys. Rev. D 23

    1982

    Earlier work this paper cites.

  • N. A. Slavnov, Teor. Mat. Fiz. 79

    1990

    Earlier work this paper cites.

Similar

  • Quantum Inverse Scattering Method and Correlation Functions

    V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin · 1993

    Cited alongside, same era.

  • O. Tsuchiya, J. Math. Phys. 39

    1998

    Cited alongside, same era.

  • N. Kitanine, J. M. Maillet, and V. Terras, Nucl. Phys. B 554

    1999

    Cited alongside, same era.

  • K. K. Kozlowski and B. Pozsgay, J. Stat. Mech.: Th. Exp. P05021 (2012)

    2012

    Cited alongside, same era.

  • J.-S. Caux and F. H. L. Essler, Phys. Rev. Lett. 110

    2013

    Cited alongside, same era.

  • J. De Nardis, B. Wouters, M. Brockmann, and J.-S. Caux, arXiv:1308.4310 (2013)

    Original

    2013

    Cited alongside, same era.

Then

  • B. Pozsgay, arXiv:1309.4593 (2013)

    Original

    2013

    Later among the works it cites.

  • M. Fagotti and F. H. L. Essler, J. Stat. Mech.: Th. Exp. P07012 (2013)

    2013

    Later among the works it cites.

  • B. Pozsgay, J. Stat. Mech.: Th. Exp. P10028 (2013)

    2013

    Later among the works it cites.

  • M. Brockmann, arXiv:1402:1471 (2014)

    2014

    Closest in time.

  • M. Brockmann, J. De Nardis, B. Wouters, J.-S. Caux, arXiv:1403:7469 (2014)

    2014

    Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…