Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Neel state

Brockmann, M., Jean-Marie Stéphan

Published Sep 1, 2017• 15 citations
OpenAlex

Abstract

We analyze universal terms that appear in the large system size scaling of the overlap between the Neel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of g-factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction.

Related papers

Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state

Michael Brockmann, Jean-Marie Stéphan

Abstract We analyze universal terms that appear in the large system size scaling of the overlap between the Néel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of g -factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction.

arXiv:1705.08505•Journal of Physics A Mathematical and Theoretical•Jul 19, 2017•41 citations

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Christian Hagendorf, Gilles Parez

The open XXZ spin chain with the anisotropy \Delta=-\frac12 Δ = − 1 2 and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain’s ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state’s logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

arXiv:2111.15223•SciPost Physics•Jun 24, 2022•2 citations

A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states

Michael Brockmann, Jacopo De Nardis, Bram Wouters +1 more

We derive a determinant expression for overlaps of Bethe states of the XXZ spin chain with the Néel 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.

arXiv:1401.2877•Journal of Physics A Mathematical and Theoretical•Mar 24, 2014•125 citations

Universal subleading terms in ground-state fidelity from boundary conformal field theory

Lorenzo Campos Venuti, Hubert Saleur, Paolo Zanardi A

The study of the (logarithm of the) fidelity, i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants provides a valuable insight on critical phenomena. When the parameters are infinitesimally close, it is known that the leading term behaves as $O({L}^{\ensuremath{\alpha}})$ ($L$ system size), where $\ensuremath{\alpha}$ is equal to the spatial dimension $d$ for gapped systems, and otherwise depends on the critical exponents. Here we show that when parameters are changed along a critical manifold, a subleading $O(1)$ term can appear. This term, somewhat similar to the topological entanglement entropy, depends only on the system's universality class and encodes nontrivial information about the topology of the system. We relate it to universal $g$ factors and partition functions of (boundary) conformal field theory in $d=1$ and $d=2$ dimensions. Numerical checks are presented on the simple example of the $XXZ$ chain.

arXiv:0807.0104•Physical Review B•Mar 13, 2009•22 citations

Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point

S. B. Rutkevich

The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having N_{x} sites, the universal Casimir scaling function, which characterizes the leading finite-size correction term in the large-N_{x} expansion of the ground-state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime.

arXiv:1904.11324•Physical review. E•Mar 10, 2020•2 citations

Overlaps ofq-raised Néel states with XXZ Bethe states and their relation to the Lieb–Liniger Bose gas

Michael Brockmann

We present a ‘Gaudin-like’ determinant expression for overlaps of q -raised Néel states with Bethe states of the spin-1/2 XXZ chain in the non-zero-magnetization sector. The former is constructed by applying global U q ( sl 2 ) spin raising operators to the Néel state, the ground state of the antiferromagnetic Ising chain. The formulas presented are derived from recently-obtained results for the overlap of the Néel state with XXZ Bethe states (Brockmann et al , 2014 J. Phys. A: Math. Theor. 47 145003, Pozsgay, 2013 arXiv:1309.4593, Kozlowski and Pozsgay, 2012 J. Stat. Mech. P05021, Tsuchiya, 1998 J. Math. Phys. 39 5946). The determinants as well as their prefactors can be evaluated in the scaling limit of the XXZ spin chain to the Lieb–Liniger Bose gas. Within this limit a q -raised Néel state that contains finitely many down spins corresponds to the ground state of finitely many free bosons. This allows for a rigorous proof of the overlap formula of De Nardis et al (2014 Phys. Rev. A 89 033601) for Lieb–Liniger Bethe states and a Bose–Einstein condensate (BEC) state with an arbitrary even number of particles.

arXiv:1402.1471•Journal of Statistical Mechanics Theory and Experiment•May 12, 2014•79 citations
We analyze universal terms that appear in the large system size scaling of the overlap between the Neel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of g-factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction.
Abstract We analyze universal terms that appear in the large system size scaling of the overlap between the Néel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of g -factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction.
On the logarithmic bipartite fidelity of the open XXZ spin chain at Δ=−1/2Δ=-1/2Δ=−1/2
The open XXZ spin chain with the anisotropy \Delta=-\frac12 Δ = − 1 2 and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain’s ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state’s logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.
The study of the (logarithm of the) fidelity, i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants provides a valuable insight on critical phenomena. When the parameters are infinitesimally close, it is known that the leading term behaves as $O({L}^{\ensuremath{\alpha}})$ (LLL system size), where $\ensuremath{\alpha}$ is equal to the spatial dimension ddd for gapped systems, and otherwise depends on the critical exponents. Here we show that when parameters are changed along a critical manifold, a subleading O(1)O(1)O(1) term can appear. This term, somewhat similar to the topological entanglement entropy, depends only on the system's universality class and encodes nontrivial information about the topology of the system. We relate it to universal ggg factors and partition functions of (boundary) conformal field theory in d=1d=1d=1 and d=2d=2d=2 dimensions. Numerical checks are presented on the simple example of the XXZXXZXXZ chain.
The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having N_{x} sites, the universal Casimir scaling function, which characterizes the leading finite-size correction term in the large-N_{x} expansion of the ground-state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime.
We present a ‘Gaudin-like’ determinant expression for overlaps of q -raised Néel states with Bethe states of the spin-1/2 XXZ chain in the non-zero-magnetization sector. The former is constructed by applying global U q ( sl 2 ) spin raising operators to the Néel state, the ground state of the antiferromagnetic Ising chain. The formulas presented are derived from recently-obtained results for the overlap of the Néel state with XXZ Bethe states (Brockmann et al , 2014 J. Phys. A: Math. Theor. 47 145003, Pozsgay, 2013 arXiv:1309.4593, Kozlowski and Pozsgay, 2012 J. Stat. Mech. P05021, Tsuchiya, 1998 J. Math. Phys. 39 5946). The determinants as well as their prefactors can be evaluated in the scaling limit of the XXZ spin chain to the Lieb–Liniger Bose gas. Within this limit a q -raised Néel state that contains finitely many down spins corresponds to the ground state of finitely many free bosons. This allows for a rigorous proof of the overlap formula of De Nardis et al (2014 Phys. Rev. A 89 033601) for Lieb–Liniger Bethe states and a Bose–Einstein condensate (BEC) state with an arbitrary even number of particles.