arXiv:2610.04848

Mixed-state quantum geometry of dense two-color QCD matter

Kouji Kashiwa, Riki Oshima, Hiroaki Kouno

Published Oct 4, 2026• 0 citations

Abstract

We investigate an information-geometric approach to dense two-color QCD using thermal states defined as normalized Gibbs states in the two-flavor Nambu--Jona-Lasinio model at the mean-field level. The Bures metric and quantum Fisher information are constructed from thermal states associated with effective Bogoliubov--de Gennes Hamiltonians reproducing the mean-field quasiparticle spectrum. On the thermodynamic parameter manifold $(T,μ)$, where $T$ is temperature and $μ$ is quark chemical potential, we analyze information-geometric quantities including the trace of the QFI matrix and the metric-volume density. The numerical results show pronounced enhancements of both quantities near the color-superconducting phase boundary, whereas only weaker signatures are observed across the chiral crossover. By contrast, neither observable exhibits a distinct feature associated with the BEC--BCS crossover.

DOI: 10.48550/arxiv.2610.04848

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arXiv:2610.04848

Mixed-state quantum geometry of dense two-color QCD matter

Kouji Kashiwa, Riki Oshima, Hiroaki Kouno

Published Oct 4, 2026• 0 citations

arXiv HTML PDF

Abstract

(T,μ)

, where

T

is temperature and

μ

is quark chemical potential, we analyze information-geometric quantities including the trace of the QFI matrix and the metric-volume density. The numerical results show pronounced enhancements of both quantities near the color-superconducting phase boundary, whereas only weaker signatures are observed across the chiral crossover. By contrast, neither observable exhibits a distinct feature associated with the BEC--BCS crossover.

DOI: 10.48550/arxiv.2610.04848

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Quantum phases at high chemical potential in 2-flavor matrix-QC $_2$ DQuantum phases at high chemical potential in 2-flavor matrix-QC$_2$D

Nirmalendu Acharyya, Prasanjit Aich, Arkajyoti Bandyopadhyay +1 more

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arXiv:2607.16774Jul 18, 20260 citations

(T,μ)

, where

T

is temperature and

μ

g_{ht}

and related geometric observables, where

h

is a controllable post-quench Hamiltonian parameter and

t

is real time. The framework treats

h

and

t

as coordinates of an extended information manifold

(h,t)

. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

SU(1,1)

symmetry, we explicitly derive and compare the complexities arising from these three distinct measures. For the Bures and Sjöqvist metrics, analytical and numerical evaluations of the corresponding geodesics are provided, revealing characteristic scaling behaviors with respect to temperature. In the Nielsen complexity approach, we rigorously handle the gauge freedoms associated with mixed state purification and non-uniqueness unitary operations, demonstrating that the resulting complexity aligns precisely with the Bures metric. Our work provides a comparative study of the geometric complexity of finite-temperature Bose-Einstein condensates, revealing its intimate connections to symmetry structures and temperature effects in BEC systems.

Quantum phases at high chemical potential in 2-flavor matrix-QC

_2

We investigate the matrix model of two-color two-flavor QCD (matrix-QCD

_{2,2}

) in regimes with large baryon (

μ_{_B}

), isospin (

μ_{_I}

), and/or chiral (

c

) chemical potentials. In these regimes, the Hamiltonian simplifies considerably, making it possible to investigate the ground state for intermediate and strong Yang-Mills coupling. By diagonalizing the Hamiltonian using the variational techniques, we show that in regimes where

μ_{_B}

and

c

(or

μ_{_B}

and

μ_{_I}

) dominate, tuning the remaining parameters leads to quantum phase transitions (QPTs). These transitions form a complex web of phases, each of which has a ground state uniquely labelled by baryon number

B

and isospin

I

. Several of these phases are LOFF-like, characterized by a ground state carrying non-zero spin and hence spontaneously breaking rotational symmetry. These results are consistent with older effective field theory predictions by Splittorff-Son-Stephanov \cite{Splittorff:2000mm}. The fermionic content of these LOFF-like ground states consists of spin-1 di-(anti-) quarks which are analogous to Cooper pairs. We compute the spin-fraction carried by the quarks and find that it constitutes a significant portion -- in some cases nearly the entirety -- of the total spin.