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

arXiv:2505.04715 · Physical review. B./Physical review. B

Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed

Ruhanshi Barad, Qicheng Tang, Xueda Wen

Published Dec 10, 2025• 2 citations
arXivHTMLPDF

Abstract

Conformal interfaces play an important role in quantum critical systems. In closed systems, the transmission properties of conformal interfaces are typically characterized by two quantities: One is the effective central charge $c_{\text{eff}}$, which measures the amount of quantum entanglement through the interface, and the other is the transmission coefficient $c_{\text{LR}}$, which measures the energy transmission through the interface. In the present work, to characterize the transmission property of conformal interfaces in open quantum systems, we propose a third quantity $c_{\text{relax}}$, which is defined through the ratio of Liouvillian gaps with and without an interface. Physically, $c_{\text{relax}}$ measures the suppression of the relaxation rate towards a steady state when the system is subject to a local dissipation. We perform both analytical perturbation calculations and exact numerical calculations based on a free fermion chain at the critical point. It is found that $c_{\text{relax}}$ decreases monotonically with the strength of the interface. In particular, $0\le c_{\text{relax}}\le c_{\text{LR}}\le c_{\text{eff}}$, where the equalities hold if and only if the interface is totally reflective or totally transmissive. Our result for $c_{\text{relax}}$ is universal in the sense that $c_{\text{relax}}$ is independent of (i) the dissipation strength in the weak dissipation regime and (ii) the location where the local dissipation is introduced. Comparing to the previously known $c_{\text{LR}}$ and $c_{\text{eff}}$ in a closed system, our $c_{\text{relax}}$ shows a distinct behavior as a function of the interface strength, suggesting its novelty to characterize conformal interfaces in open systems and offering insights into critical systems under dissipation.

DOI
10.1103/zjh4-5n32

Related papers

Universal Suppression of Dissipation across Conformal Interface in Open Quantum Critical Systems

Ruhanshi Barad, Tian Wu, Qicheng Tang +1 more

Conformal interfaces provide an important setting for studying universal transmission phenomena in one-dimensional quantum critical systems. While energy and information transmission across such interfaces are characterized by universal quantities in closed systems, the corresponding role of conformal interfaces in dissipative dynamics is less understood. In this work, we study relaxation in locally dissipative quantum critical chains with a conformal interface and show that a universal characterization emerges at the level of individual relaxation modes. We first show that the relaxation coefficient defined in the recent work [1] from the Liouvillian gap can become non-universal for certain boundary conditions because the mode determining the smallest decay rate can change as the interface transmission is varied. To resolve this ambiguity, we introduce a mode-resolved relaxation coefficient $c_{\rm relax}$ by continuously tracking the same Liouvillian rapidity mode as a function of the interface transmission. Using analytical and numerical calculations for a critical harmonic chain and a critical free-fermion chain, we find that, in the weak-dissipation regime, $c_{\rm relax}$ follows the same universal dependence on the interface transmission in all cases considered, independent of microscopic details such as the boundary conditions, dissipation strength, and location of the local dissipation. For boundary dissipation, this universal behavior persists even at finite dissipation strength. Our results establish a universal mode-resolved characterization of relaxation across conformal interfaces in open quantum critical systems.

cond-mat.stat-mechCross-listedarXiv:2609.19292•Sep 18, 2026•0 citations

Entanglement evolution across a conformal interface

Xueda Wen, Yuxuan Wang, Shinsei Ryu

Abstract For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A , and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.

arXiv:1711.02126•Journal of Physics A Mathematical and Theoretical•Mar 9, 2018•26 citations

Universal Bound on Effective Central Charge and Its Saturation

Andreas Karch, Yuya Kusuki, Hirosi Ooguri +2 more

The effective central charge (denoted by c_{eff}) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient c_{LR} of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this Letter, we propose the inequalities, 0≤c_{LR}≤c_{eff}≤min(c_{L},c_{R}). They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.

arXiv:2404.01515•Physical Review Letters•Aug 30, 2024•16 citations

Colliders and conformal interfaces

Marco Meineri, João Penedones, Antonin Rousset

Abstract We set up a scattering experiment of matter against an impurity which separates two generic one-dimensional critical quantum systems. We compute the flux of reflected and transmitted energy, thus defining a precise measure of the transparency of the interface between the related two-dimensional conformal field theories. If the largest symmetry algebra is Virasoro, we find that the reflection and transmission coefficients are independent of the details of the initial state, and are fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present. Positivity of the total energy flux at infinity imposes bounds on the coefficient of the two-point function of the displacement operator, which controls the free-energy cost of a small deformation of the interface. Finally, we study out-of-equilibrium steady states of a critical system connecting two reservoirs at different temperatures. In the absence of extended symmetries, our result implies that the energy flux across an impurity is proportional to the difference of the squared temperatures and controlled by the reflection coefficient.

arXiv:1904.10974•Journal of High Energy Physics•Feb 1, 2020•49 citations

Universality of Dissipation across Holographic Interfaces

Andreas Karch, Mianqi Wang

Motivated by recent results in spin chains we study dissipation and relaxation in a two-dimensional \ak{holographic} interface conformal field theory (ICFT) in which degrees of freedom on one side of the interface are coupled to an external bath, while the other side remains isolated. In the bulk description this setup is realized by gluing a supersymmetric Janus geometry to a BTZ black hole region, with the coupling implemented through a double-trace deformation. We determine the quasinormal modes in the bulk by solving the double-trace matching conditions of the system and bath. Focusing on the fixed AdS$_2$ descendant channel at large frequency, we introduce the dimensionless ratio $c_{UV}$ as a projected measure of interface-induced suppression of dissipation rate. Analytically we find that in this limit, $c_{UV}$ is independent of coupling details to the bath. It is a strong candidate for a universal interface observable characterizing dissipation and relaxation across the interface, in additional to the $c_{\rm relax}$ raised in earlier work for lattice models.

arXiv:2601.16888•Jan 23, 2026•0 citations

Universal entanglement signatures of interface conformal field theories

Qicheng Tang, Zixia Wei, Y. C. Tang +2 more

An interface connecting two distinct conformal field theories hosts rich critical behaviors. In this paper, we investigate the entanglement properties of such critical interface theories for probing the underlying universality. As inspired by holographic perspectives, we demonstrate vital features of various entanglement measures regarding such interfaces based on several paradigmatic lattice models. Crucially, for two subsystems adjacent at the interface, the mutual information and the reflected entropy exhibit identical leading logarithmic scaling, giving an effective interface central charge that takes the same value as the smaller central charge of the two conformal field theories. Our paper demonstrates that the entanglement measure offers a powerful tool to explore the rich physics in critical interface theories.

arXiv:2308.03646•Physical review. B./Physical review. B•Jan 8, 2024•15 citations
Conformal interfaces play an important role in quantum critical systems. In closed systems, the transmission properties of conformal interfaces are typically characterized by two quantities: One is the effective central charge ceffc_{\text{eff}}ceff​, which measures the amount of quantum entanglement through the interface, and the other is the transmission coefficient cLRc_{\text{LR}}cLR​, which measures the energy transmission through the interface. In the present work, to characterize the transmission property of conformal interfaces in open quantum systems, we propose a third quantity crelaxc_{\text{relax}}crelax​, which is defined through the ratio of Liouvillian gaps with and without an interface. Physically, crelaxc_{\text{relax}}crelax​ measures the suppression of the relaxation rate towards a steady state when the system is subject to a local dissipation. We perform both analytical perturbation calculations and exact numerical calculations based on a free fermion chain at the critical point. It is found that crelaxc_{\text{relax}}crelax​ decreases monotonically with the strength of the interface. In particular, 0≤crelax≤cLR≤ceff0\le c_{\text{relax}}\le c_{\text{LR}}\le c_{\text{eff}}0≤crelax​≤cLR​≤ceff​, where the equalities hold if and only if the interface is totally reflective or totally transmissive. Our result for crelaxc_{\text{relax}}crelax​ is universal in the sense that crelaxc_{\text{relax}}crelax​ is independent of (i) the dissipation strength in the weak dissipation regime and (ii) the location where the local dissipation is introduced. Comparing to the previously known cLRc_{\text{LR}}cLR​ and ceffc_{\text{eff}}ceff​ in a closed system, our crelaxc_{\text{relax}}crelax​ shows a distinct behavior as a function of the interface strength, suggesting its novelty to characterize conformal interfaces in open systems and offering insights into critical systems under dissipation.
Conformal interfaces provide an important setting for studying universal transmission phenomena in one-dimensional quantum critical systems. While energy and information transmission across such interfaces are characterized by universal quantities in closed systems, the corresponding role of conformal interfaces in dissipative dynamics is less understood. In this work, we study relaxation in locally dissipative quantum critical chains with a conformal interface and show that a universal characterization emerges at the level of individual relaxation modes. We first show that the relaxation coefficient defined in the recent work [1] from the Liouvillian gap can become non-universal for certain boundary conditions because the mode determining the smallest decay rate can change as the interface transmission is varied. To resolve this ambiguity, we introduce a mode-resolved relaxation coefficient crelaxc_{\rm relax}crelax​ by continuously tracking the same Liouvillian rapidity mode as a function of the interface transmission. Using analytical and numerical calculations for a critical harmonic chain and a critical free-fermion chain, we find that, in the weak-dissipation regime, crelaxc_{\rm relax}crelax​ follows the same universal dependence on the interface transmission in all cases considered, independent of microscopic details such as the boundary conditions, dissipation strength, and location of the local dissipation. For boundary dissipation, this universal behavior persists even at finite dissipation strength. Our results establish a universal mode-resolved characterization of relaxation across conformal interfaces in open quantum critical systems.
Abstract For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A , and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.
The effective central charge (denoted by c_{eff}) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient c_{LR} of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this Letter, we propose the inequalities, 0≤c_{LR}≤c_{eff}≤min(c_{L},c_{R}). They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.
Abstract We set up a scattering experiment of matter against an impurity which separates two generic one-dimensional critical quantum systems. We compute the flux of reflected and transmitted energy, thus defining a precise measure of the transparency of the interface between the related two-dimensional conformal field theories. If the largest symmetry algebra is Virasoro, we find that the reflection and transmission coefficients are independent of the details of the initial state, and are fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present. Positivity of the total energy flux at infinity imposes bounds on the coefficient of the two-point function of the displacement operator, which controls the free-energy cost of a small deformation of the interface. Finally, we study out-of-equilibrium steady states of a critical system connecting two reservoirs at different temperatures. In the absence of extended symmetries, our result implies that the energy flux across an impurity is proportional to the difference of the squared temperatures and controlled by the reflection coefficient.
Motivated by recent results in spin chains we study dissipation and relaxation in a two-dimensional \ak{holographic} interface conformal field theory (ICFT) in which degrees of freedom on one side of the interface are coupled to an external bath, while the other side remains isolated. In the bulk description this setup is realized by gluing a supersymmetric Janus geometry to a BTZ black hole region, with the coupling implemented through a double-trace deformation. We determine the quasinormal modes in the bulk by solving the double-trace matching conditions of the system and bath. Focusing on the fixed AdS2_22​ descendant channel at large frequency, we introduce the dimensionless ratio cUVc_{UV}cUV​ as a projected measure of interface-induced suppression of dissipation rate. Analytically we find that in this limit, cUVc_{UV}cUV​ is independent of coupling details to the bath. It is a strong candidate for a universal interface observable characterizing dissipation and relaxation across the interface, in additional to the crelaxc_{\rm relax}crelax​ raised in earlier work for lattice models.
An interface connecting two distinct conformal field theories hosts rich critical behaviors. In this paper, we investigate the entanglement properties of such critical interface theories for probing the underlying universality. As inspired by holographic perspectives, we demonstrate vital features of various entanglement measures regarding such interfaces based on several paradigmatic lattice models. Crucially, for two subsystems adjacent at the interface, the mutual information and the reflected entropy exhibit identical leading logarithmic scaling, giving an effective interface central charge that takes the same value as the smaller central charge of the two conformal field theories. Our paper demonstrates that the entanglement measure offers a powerful tool to explore the rich physics in critical interface theories.