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:2407.10884 · Physical review. B./Physical review. B

Effect of order of transfer matrix exceptional points on transport at band edges

Madhumita Saha, Bijay Kumar Agarwalla, Manas Kulkarni, Archak Purkayastha

Published Mar 19, 2025• 3 citations
arXivHTMLPDF

Abstract

Recently, it has been shown that, in one-dimensional fermionic systems, close to band edges, the zero temperature conductance scales as $1/{N}^{2}$, where $N$ is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occurs at every band edge. Further, in the presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with $N$ over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in the absence of bulk dephasing, surprisingly, the universal $1/{N}^{2}$ scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In the presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime, and the exponent of superballistic scaling all encode the order of the transfer matrix EP.

DOI
10.1103/physrevb.111.125412

Related papers

Environment assisted superballistic scaling of conductance

Madhumita Saha, Bijay Kumar Agarwalla, Manas Kulkarni +1 more

We find that, in the presence of weak incoherent effects from surrounding environments, the low-temperature conductance of nearest-neighbor tight-binding fermionic chains exhibits a counter-intuitive monotonic growth with system length when Fermi energy is near the band edges, indicating a superballistic scaling. This fascinating environment-assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This regime can be systematically expanded by decreasing the coupling to the surrounding environments and by reducing temperature. This behavior is robust against weak disorder and slight shifts from band edge, although the extent of the superballistic scaling regime is affected by them. We give precise predictions of how the superballistic scaling regime depends on coupling to surrounding environments, disorder strength, shifts from band edge, and temperature. There is no corresponding analog of this behavior in isolated systems. The superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band edge.

arXiv:2208.04269•Physical review. B./Physical review. B•Oct 31, 2023•7 citations

Topologically protected subdiffusive transport in two-dimensional fermionic wires

Junaid Majeed Bhat

The conductance at the band edges of one-dimensional fermionic wires, with $N$ sites, has been shown to have subdiffusive $(1/{N}^{2})$ behavior. We investigate this issue in two-dimensional fermionic wires described by a hopping model on an ${N}_{x}\ifmmode\times\else\texttimes\fi{}{N}_{y}$ rectangular lattice comprised of vertical chains with a Hermitian intrachain and interchain hopping matrices given by ${H}_{0}$ and ${H}_{1}$, respectively. We study particle transport using the nonequilibrium Green's function formalism, and we show that the asymptotic behavior of the conductance, $T(\ensuremath{\omega})$, at the Fermi level $\ensuremath{\omega}$, is controlled by the spectrum of a dimensionless matrix $A(\ensuremath{\omega})=(\ensuremath{-}\ensuremath{\omega}+{H}_{0}){H}_{1}^{\ensuremath{-}1}$. This gives three simple conditions on the spectrum of $A(\ensuremath{\omega})$ for observing ballistic, subdiffusive, and exponentially decaying $T(\ensuremath{\omega})$ with respect to ${N}_{x}$. We show that certain eigenvalues of $A(\ensuremath{\omega})$ give rise to subdiffusive contributions in the conductance, and correspond to the band edges of the isolated wire. We demonstrate that the condition for observing the subdiffusive behavior can be satisfied if $A(\ensuremath{\omega})$ has nontrivial topology. In that case, a transition from ballistic behavior to subdiffusive behavior of the conductance is observed as the hopping parameters are tuned within the topological regime. We argue that at the transition point, different behaviors of the conductance can arise as the trivial bulk bands of $A(\ensuremath{\omega})$ also contribute subdiffusively. We illustrate our findings in a simple model by numerically computing the variation of the conductance with ${N}_{x}$. Our numerical results indicate a different subdiffusive behavior ($1/{N}_{x}^{3}$) of the conductance at the transition point. We find the numerical results to be in good agreement with the theoretical predictions.

arXiv:2310.08474•Physical review. B./Physical review. B•Mar 14, 2024•2 citations

Anomalous transport in quasiperiodic lattices: emergent exceptional points at band edges and log-periodic oscillations

Jinyuan Shang, Haiping Hu

Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of $\mathcal{G}_{\text{typ}}\sim L^{-2}$ with system size $L$. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.

cond-mat.mes-hallCross-listedarXiv:2601.10056•Jan 16, 2026

Subdiffusive Phases in Open Clean Long-Range Systems

Archak Purkayastha, Madhumita Saha, Bijay Kumar Agarwalla

We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing subdiffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e., in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known nonequilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the subdiffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing subdiffusive scaling of conductance with system size in a two-terminal setup are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.

arXiv:2105.04539•Physical Review Letters•Dec 6, 2021•18 citations

Transport in open quantum systems in the presence of lossy channels

Katha Ganguly, Manas Kulkarni, Bijay Kumar Agarwalla

We study nonequilibrium steady-state transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-Hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.

Physical review. B./Physical review. B•Dec 24, 2024•11 citations

Edge states enhanced by long-range hopping: An analytical study*

Huiping Wang, Li Ren, Li‐Guo Qin +1 more

We analyze the behavior of edge states in long-range (LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method (TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in one- and two-dimensional (2D) superconductors with LR hopping and pairing.

Chinese Physics B•Feb 25, 2021•3 citations
Recently, it has been shown that, in one-dimensional fermionic systems, close to band edges, the zero temperature conductance scales as 1/N21/{N}^{2}1/N2, where NNN is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occurs at every band edge. Further, in the presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with NNN over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in the absence of bulk dephasing, surprisingly, the universal 1/N21/{N}^{2}1/N2 scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In the presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime, and the exponent of superballistic scaling all encode the order of the transfer matrix EP.
We find that, in the presence of weak incoherent effects from surrounding environments, the low-temperature conductance of nearest-neighbor tight-binding fermionic chains exhibits a counter-intuitive monotonic growth with system length when Fermi energy is near the band edges, indicating a superballistic scaling. This fascinating environment-assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This regime can be systematically expanded by decreasing the coupling to the surrounding environments and by reducing temperature. This behavior is robust against weak disorder and slight shifts from band edge, although the extent of the superballistic scaling regime is affected by them. We give precise predictions of how the superballistic scaling regime depends on coupling to surrounding environments, disorder strength, shifts from band edge, and temperature. There is no corresponding analog of this behavior in isolated systems. The superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band edge.
The conductance at the band edges of one-dimensional fermionic wires, with NNN sites, has been shown to have subdiffusive (1/N2)(1/{N}^{2})(1/N2) behavior. We investigate this issue in two-dimensional fermionic wires described by a hopping model on an ${N}_{x}\ifmmode\times\else\texttimes\fi{}{N}_{y}$ rectangular lattice comprised of vertical chains with a Hermitian intrachain and interchain hopping matrices given by H0{H}_{0}H0​ and H1{H}_{1}H1​, respectively. We study particle transport using the nonequilibrium Green's function formalism, and we show that the asymptotic behavior of the conductance, $T(\ensuremath{\omega})$, at the Fermi level $\ensuremath{\omega}$, is controlled by the spectrum of a dimensionless matrix $A(\ensuremath{\omega})=(\ensuremath{-}\ensuremath{\omega}+{H}_{0}){H}_{1}^{\ensuremath{-}1}$. This gives three simple conditions on the spectrum of $A(\ensuremath{\omega})$ for observing ballistic, subdiffusive, and exponentially decaying $T(\ensuremath{\omega})$ with respect to Nx{N}_{x}Nx​. We show that certain eigenvalues of $A(\ensuremath{\omega})$ give rise to subdiffusive contributions in the conductance, and correspond to the band edges of the isolated wire. We demonstrate that the condition for observing the subdiffusive behavior can be satisfied if $A(\ensuremath{\omega})$ has nontrivial topology. In that case, a transition from ballistic behavior to subdiffusive behavior of the conductance is observed as the hopping parameters are tuned within the topological regime. We argue that at the transition point, different behaviors of the conductance can arise as the trivial bulk bands of $A(\ensuremath{\omega})$ also contribute subdiffusively. We illustrate our findings in a simple model by numerically computing the variation of the conductance with Nx{N}_{x}Nx​. Our numerical results indicate a different subdiffusive behavior (1/Nx31/{N}_{x}^{3}1/Nx3​) of the conductance at the transition point. We find the numerical results to be in good agreement with the theoretical predictions.
Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of Gtyp∼L−2\mathcal{G}_{\text{typ}}\sim L^{-2}Gtyp​∼L−2 with system size LLL. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.
We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing subdiffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e., in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known nonequilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the subdiffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing subdiffusive scaling of conductance with system size in a two-terminal setup are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.
We study nonequilibrium steady-state transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-Hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.
We analyze the behavior of edge states in long-range (LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method (TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in one- and two-dimensional (2D) superconductors with LR hopping and pairing.