We investigate the non-equilibrium topology of the steady state of a periodically driven, dissipative Su-Schrieffer-Heeger (SSH) chain using the ensemble geometric phase (EGP) $φ_{\mathrm{EGP}}$ , a generalisation of the Zak phase to mixed states. The coupling to thermal reservoirs is treated microscopically within Floquet-Born-Markov theory without the rotating-wave approximation. We classify the steady state rather than the generator of the dynamics, using its purity spectrum as the analogue of a band structure. We show that, within the EGP framework, the $\mathbb{Z}\times\mathbb{Z}$ structure of isolated chiral-symmetric Floquet SSH systems generally does not carry over to the steady state. Instead, the steady state carries a single invariant whose type is set by an underlying symmetry. When this symmetry holds, the invariant is $\mathbb{Z}_2$ -valued, with quantised $φ_{\mathrm{EGP}}=\pmπ/2$ at all times and finite temperatures. The EGP can switch within a driving period, tracking the presence of edge modes in the open-boundary purity spectrum and thereby establishing a bulk-boundary correspondence. The fraction of each period spent in the nontrivial regime varies continuously with the driving frequency, and the switching disappears if the dependence of the dissipator on the drive is neglected. When the symmetry is broken, $φ_{\mathrm{EGP}}$ is no longer quantised, but its winding over a drive period $T$ defines an invariant $ν_T \in \mathbb Z$ , with no purity-spectrum bulk-boundary correspondence. We propose that its changes signal temperature- and frequency-driven topological phase transitions. Our formalism extends to general quadratic fermionic systems with linear bath couplings.We investigate the non-equilibrium topology of the steady state of a periodically driven, dissipative Su-Schrieffer-Heeger (SSH) chain using the ensemble geometric phase (EGP) $φ_{\mathrm{EGP}}$, a generalisation of the Zak phase to mixed states. The coupling to thermal reservoirs is treated microscopically within Floquet-Born-Markov theory without the rotating-wave approximation. We classify the steady state rather than the generator of the dynamics, using its purity spectrum as the analogue of a band structure. We show that, within the EGP framework, the $\mathbb{Z}\times\mathbb{Z}$ structure of isolated chiral-symmetric Floquet SSH systems generally does not carry over to the steady state. Instead, the steady state carries a single invariant whose type is set by an underlying symmetry. When this symmetry holds, the invariant is $\mathbb{Z}_2$-valued, with quantised $φ_{\mathrm{EGP}}=\pmπ/2$ at all times and finite temperatures. The EGP can switch within a driving period, tracking the presence of edge modes in the open-boundary purity spectrum and thereby establishing a bulk-boundary correspondence. The fraction of each period spent in the nontrivial regime varies continuously with the driving frequency, and the switching disappears if the dependence of the dissipator on the drive is neglected. When the symmetry is broken, $φ_{\mathrm{EGP}}$ is no longer quantised, but its winding over a drive period $T$ defines an invariant $ν_T \in \mathbb Z$, with no purity-spectrum bulk-boundary correspondence. We propose that its changes signal temperature- and frequency-driven topological phase transitions. Our formalism extends to general quadratic fermionic systems with linear bath couplings.

cond-mat.mes-hallCross-listedarXiv:2604.25248Apr 29, 20260 citations

Generalized Quasi-Energies and Floquet States for a Dissipative System

R. Graham, R. Hubner

Annals of PhysicsSep 1, 199422 citations

Investigating Floquet dynamics in driven Fermi-Hubbard systems

Frederik Görg, Michael Messer, Kilian Sandholzer +5 more

Bulletin of the American Physical SocietyMay 30, 20190 citations

Signatures of quantum phases in a dissipative system

Rohan Joshi, Saikat Mondal, Souvik Kumar Bandyopadhyay +2 more

Lindbladian formalism, as tuned to dissipative and open systems, has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model-where the bath acts both as a source and a sink of fermionic particles with different coupling rates. As a function of these two couplings, we investigate the steady state, its entanglement content, and its approach from varying initial states. Interestingly, we find that the steady state phase diagram retains decipherable signatures of ground state critical physics. We also show that early-time fidelity is a useful marker to find a subclass of phase transitions in such situations. Moreover, we show that the survival of critical signatures at late-times, strongly depend on the thermal nature of the steady state. This connection hints at a correspondence between quantum observables and classical magnetism in the steady state of such systems. Our work uncovers interesting connections between dissipative quantum many-body systems, thermalization of a classical spin and many-body quantum critical phenomena.Lindbladian formalism, as tuned to dissipative and open systems, has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model-where the bath acts both as a source and a sink of fermionic particles with different coupling rates. As a function of these two couplings, we investigate the steady state, its entanglement content, and its approach from varying initial states. Interestingly, we find that the steady state phase diagram retains decipherable signatures of ground state critical physics. We also show that early-time fidelity is a useful marker to find a subclass of phase transitions in such situations. Moreover, we show that the survival of critical signatures at late-times, strongly depend on the thermal nature of the steady state. This connection hints at a correspondence between quantum observables and classical magnetism in the steady state of such systems. Our work uncovers interesting connections between dissipative quantum many-body systems, thermalization of a classical spin and many-body quantum critical phenomena.

arXiv:2312.17166Journal of Physics Condensed MatterMar 18, 20242 citations

We investigate the non-equilibrium topology of the steady state of a periodically driven, dissipative Su-Schrieffer-Heeger (SSH) chain using the ensemble geometric phase (EGP)

φ_{\mathrm{EGP}}

, a generalisation of the Zak phase to mixed states. The coupling to thermal reservoirs is treated microscopically within Floquet-Born-Markov theory without the rotating-wave approximation. We classify the steady state rather than the generator of the dynamics, using its purity spectrum as the analogue of a band structure. We show that, within the EGP framework, the

\mathbb{Z}\times\mathbb{Z}

structure of isolated chiral-symmetric Floquet SSH systems generally does not carry over to the steady state. Instead, the steady state carries a single invariant whose type is set by an underlying symmetry. When this symmetry holds, the invariant is

\mathbb{Z}_2

-valued, with quantised

φ_{\mathrm{EGP}}=\pmπ/2

at all times and finite temperatures. The EGP can switch within a driving period, tracking the presence of edge modes in the open-boundary purity spectrum and thereby establishing a bulk-boundary correspondence. The fraction of each period spent in the nontrivial regime varies continuously with the driving frequency, and the switching disappears if the dependence of the dissipator on the drive is neglected. When the symmetry is broken,

φ_{\mathrm{EGP}}

is no longer quantised, but its winding over a drive period

T

defines an invariant

ν_T \in \mathbb Z

, with no purity-spectrum bulk-boundary correspondence. We propose that its changes signal temperature- and frequency-driven topological phase transitions. Our formalism extends to general quadratic fermionic systems with linear bath couplings.