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:2207.08243 · Physical review. B./Physical review. B

Stable bipolarons in open quantum systems

Mattia Moroder, M. Grundner, François Damanet, Ulrich Schollwöck, Sam Mardazad, Stuart Flannigan, Thomas Köhler, Sebastian Paeckel

Published Jun 29, 2023• 15 citations
arXivHTMLPDF

Abstract

Recent advances in numerical methods significantly pushed forward the understanding of electrons coupled to quantized lattice vibrations. At this stage, it becomes increasingly important to also account for the effects of physically inevitable environments. Here, we combine state-of-the-art tensor-network and quantum trajectories methods in order to study the impact of dissipation on realistic condensed matter models including highly excited phononic modes. In particular, we study the transport properties of the Hubbard-Holstein Hamiltonian that models a large class of materials characterized by strong electron-phonon coupling, in contact with a dissipative environment. We combine the non-Markovian hierarchy of pure states method and the Markovian quantum jumps method with the newly introduced projected purified density-matrix renormalization group, creating powerful tensor-network methods for dissipative quantum many-body systems. Investigating their numerical properties, we find a significant speedup up to a factor $\ensuremath{\approx}30$ compared to conventional tensor-network techniques. We apply these methods to study dissipative quenches, aiming for an in-depth understanding of the formation, stability, and quasiparticle properties of bipolarons. Surprisingly, our results show that in the metallic phase dissipation localizes the bipolarons, which is reminiscent of an indirect quantum Zeno effect. However, the bipolaronic binding energy remains mainly unaffected, even in the presence of strong dissipation, exhibiting remarkable bipolaron stability. These findings shed light on the problem of designing real materials exhibiting phonon-mediated high-${T}_{\mathrm{C}}$ superconductivity.

DOI
10.1103/physrevb.107.214310

Related papers

Many-Body Quantum State Diffusion for Non-Markovian Dynamics in Strongly Interacting Systems

S. Flannigan, F. Damanet, A. J. Daley

Capturing non-Markovian dynamics of open quantum systems is generally a challenging problem, especially for strongly interacting many-body systems. In this Letter, we combine recently developed non-Markovian quantum state diffusion techniques with tensor network methods to address this challenge. As a first example, we explore a Hubbard-Holstein model with dissipative phonon modes, where this new approach allows us to quantitatively assess how correlations spread in the presence of non-Markovian dissipation in a 1D many-body system. We find regimes where correlation growth can be enhanced by these effects, offering new routes for dissipatively enhancing transport and correlation spreading, relevant for both solid state and cold atom experiments.

arXiv:2108.06224•Physical Review Letters•Feb 8, 2022•48 citations

Quantum Phase Transitions in the 1D Bose-Hubbard Model: From Local Interactions to Cavity-Mediated Dissipation

Muhammad Haris Zafar

The Bose-Hubbard model provides a foundational paradigm for exploring quantum phase transitions in many-body systems. This thesis presents a systematic investigation into this model and its extensions, designed to provide a clear path for understanding both the rich underlying physics and the sophisticated numerical methods required for its study. Our approach is sequential: we begin with the standard one-dimensional Bose-Hubbard model, introduce complexity via the extended model with long-range interactions, and conclude by analyzing the impact of dissipation in a cavity-coupled open quantum system.To navigate these regimes, we implement and apply a suite of powerful computational techniques, including Density Matrix Renormalization Group (DMRG), finite-temperature Quantum Monte Carlo (QMC), and Mean-Field Theory (MFT). A significant component of this work is the detailed exposition of the implementation and logic of these numerical methods. Through their comparative application, we precisely characterize the equilibrium phase diagrams and benchmark the capabilities of each method. Crucially, our analysis of the open-system dynamics reveals that dissipation replaces the equilibrium phase diagram with one governed by non-equilibrium steady states (NESS), where the system evolves to either a stable solution or a persistent limit cycle.As such, this thesis is intended to serve a dual purpose: it is both a rigorous physical study of quantum phase transitions in a condensed matter system and a selfcontained pedagogical guide for researchers beginning to explore the phenomenology of quantum phase transitions through numerical schemes.

•Sep 6, 2026•0 citations

Cooper-Paired Bipolaronic Superconductors

Grundner, Martin, Tizian Blatz, John Sous +2 more

Light-mass bipolarons in off-diagonally coupled electron-phonon systems provide a potential route to bipolaronic high-Tc superconductivity. While there has been numerical progress in the physically relevant limit of slow phonons, more insights are needed to fully understand to what extent this mechanism survives at finite densities and in different regimes. We address these questions using advanced tensor-network methods applied to the Su-Schrieffer-Heeger model. Studying both the spectral properties of isolated bipolarons as well as the pairing correlations at small finite densities, we find evidence that the conventional picture of bipolarons as molecular bound states which undergo Bose-Einstein condensation may need to be reconsidered. Instead, our findings suggest correlation-driven formation of a fragmented condensate with spatially separated polaron pairs, stabilized by strong repulsive electron-electron interactions at moderate values of the electron-phonon coupling. These spatially modulated charge clouds exhibit pairing with a typical length-scale set by the Fermi momentum.

arXiv:2308.13427•Aug 25, 2023•1 citation

Tensor network simulations of open quantum systems

Dainius Kilda

The nonequilibrium effects of dissipation and drive play a key role in an immense variety of nanoscale and mesoscale quantum systems. To understand the behaviour of open quantum systems, we need accurate methods that capture the influence of the environment on the system, while managing the exponentially large Hilbert space required to describe the system. Tensor network algorithms offer an efficient way to approach this challenge. In this thesis, we develop and apply tensor network techniques to study the dynamics and steady states of various open quantum systems. The first part of the thesis focuses on the driven dissipative many body physics in coupled cavity arrays described by Born-Markov master equations. We extend transfer matrix product operator methods to Liouvillian dynamics, and utilize them to compute dynamical correlation functions and fluorescence spectrum of an infinite coupled cavity array in 1D. We also investigate thermalization, and observe the emergence of a quasi-thermal steady state with a negative effective temperature. In another study, we use infinite projected entangled pair state (iPEPS) methods to compute steady states of coupled cavity lattices in 2D. We find that a straightforward adaptation of iPEPS to Liouvillian dynamics is unstable, contradicting a recent publication in the field. The second part investigates more general systems involving strong couplings and structured environments that induce non-Markovian dynamics. We develop a powerful time-evolving matrix product operator (TEMPO) algorithm that builds on Feynman-Vernon influence functional formalism, and uses matrix product states (MPS) to represent the temporal non-Markovian correlations efficiently. We apply TEMPO to study the localization phase transition of the spin-boson model and the dynamics of two spatially separated two-level systems coupled to a common environment. Finally, we propose the Toblerone TEMPO algorithm, which extends TEMPO to many-body systems interacting with general bosonic environments.

•Mar 3, 2020•0 citations

Light bipolarons in a system of electrons coupled to dispersive optical phonons

K. Kovač, J. Bonča

We investigate the ground-state properties of the bipolaron coupled to quantum dispersive optical phonons in the one-dimensional Holstein-Hubbard model. We concentrate on the interplay between the phonon dispersion and the Coulomb repulsion and their mutual effect on the bipolaron effective mass, the binding energy, and the phase diagram. Most surprisingly, the sign of the curvature of the optical phonon dispersion plays a decisive role in the bipolaron binding energy in the presence of the Coulomb repulsion $U$. In particular, when the sign of the phonon dispersion curvature matches the sign of the electron dispersion curvature, the bipolaron remains bound in the strong-coupling limit even when $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and the binding emanates from the exchange of phonons between two electrons residing on adjacent sites. At moderate electron-phonon coupling a light bipolaron exists up to large values of $U$. Finally, an intuitive explanation of the role of the phonon dispersion on the bipolaron binding energy is derived using the strong-coupling limit where the binding emanates from the exchange of phonons between two electrons residing on adjacent sites which leads to enhanced stability of bipolarons at elevated Coulomb repulsion.

arXiv:2311.12403•Physical review. B./Physical review. B•Feb 12, 2024•4 citations

Transport and dynamical properties of electron-phonon coupled systems

D. J. Jansen

In this thesis, I investigate the transport and dynamical properties of electron-phonon coupled systems using numerical methods. I focus on the one-dimensional Holstein model, which incorporates both polaron and charge density wave (CDW) physics, and use matrix-product-state-based algorithms. In the first part, I present work where we combine purification with local basis optimization to study the finite-temperature properties of the model. This gives access to polaron spectral functions, polaron and bipolaron optical conductivity, and the energy-transport coefficient at finite filling. The second part focuses on the Holstein model coupled to two tight-binding leads. There, we investigate how current is transported through the structure and how CDW states break down. In the last part, we analyze the spread of an electron in a lattice and the decay of CDWs. We aim to understand if a full quantum mechanical treatment of the phonons is necessary or if trajectory-based algorithms are applicable.

•Jan 1, 2023•0 citations
Recent advances in numerical methods significantly pushed forward the understanding of electrons coupled to quantized lattice vibrations. At this stage, it becomes increasingly important to also account for the effects of physically inevitable environments. Here, we combine state-of-the-art tensor-network and quantum trajectories methods in order to study the impact of dissipation on realistic condensed matter models including highly excited phononic modes. In particular, we study the transport properties of the Hubbard-Holstein Hamiltonian that models a large class of materials characterized by strong electron-phonon coupling, in contact with a dissipative environment. We combine the non-Markovian hierarchy of pure states method and the Markovian quantum jumps method with the newly introduced projected purified density-matrix renormalization group, creating powerful tensor-network methods for dissipative quantum many-body systems. Investigating their numerical properties, we find a significant speedup up to a factor \ensuremath≈30\ensuremath{\approx}30\ensuremath≈30 compared to conventional tensor-network techniques. We apply these methods to study dissipative quenches, aiming for an in-depth understanding of the formation, stability, and quasiparticle properties of bipolarons. Surprisingly, our results show that in the metallic phase dissipation localizes the bipolarons, which is reminiscent of an indirect quantum Zeno effect. However, the bipolaronic binding energy remains mainly unaffected, even in the presence of strong dissipation, exhibiting remarkable bipolaron stability. These findings shed light on the problem of designing real materials exhibiting phonon-mediated high-TC{T}_{\mathrm{C}}TC​ superconductivity.
Capturing non-Markovian dynamics of open quantum systems is generally a challenging problem, especially for strongly interacting many-body systems. In this Letter, we combine recently developed non-Markovian quantum state diffusion techniques with tensor network methods to address this challenge. As a first example, we explore a Hubbard-Holstein model with dissipative phonon modes, where this new approach allows us to quantitatively assess how correlations spread in the presence of non-Markovian dissipation in a 1D many-body system. We find regimes where correlation growth can be enhanced by these effects, offering new routes for dissipatively enhancing transport and correlation spreading, relevant for both solid state and cold atom experiments.
The Bose-Hubbard model provides a foundational paradigm for exploring quantum phase transitions in many-body systems. This thesis presents a systematic investigation into this model and its extensions, designed to provide a clear path for understanding both the rich underlying physics and the sophisticated numerical methods required for its study. Our approach is sequential: we begin with the standard one-dimensional Bose-Hubbard model, introduce complexity via the extended model with long-range interactions, and conclude by analyzing the impact of dissipation in a cavity-coupled open quantum system.To navigate these regimes, we implement and apply a suite of powerful computational techniques, including Density Matrix Renormalization Group (DMRG), finite-temperature Quantum Monte Carlo (QMC), and Mean-Field Theory (MFT). A significant component of this work is the detailed exposition of the implementation and logic of these numerical methods. Through their comparative application, we precisely characterize the equilibrium phase diagrams and benchmark the capabilities of each method. Crucially, our analysis of the open-system dynamics reveals that dissipation replaces the equilibrium phase diagram with one governed by non-equilibrium steady states (NESS), where the system evolves to either a stable solution or a persistent limit cycle.As such, this thesis is intended to serve a dual purpose: it is both a rigorous physical study of quantum phase transitions in a condensed matter system and a selfcontained pedagogical guide for researchers beginning to explore the phenomenology of quantum phase transitions through numerical schemes.
Light-mass bipolarons in off-diagonally coupled electron-phonon systems provide a potential route to bipolaronic high-Tc superconductivity. While there has been numerical progress in the physically relevant limit of slow phonons, more insights are needed to fully understand to what extent this mechanism survives at finite densities and in different regimes. We address these questions using advanced tensor-network methods applied to the Su-Schrieffer-Heeger model. Studying both the spectral properties of isolated bipolarons as well as the pairing correlations at small finite densities, we find evidence that the conventional picture of bipolarons as molecular bound states which undergo Bose-Einstein condensation may need to be reconsidered. Instead, our findings suggest correlation-driven formation of a fragmented condensate with spatially separated polaron pairs, stabilized by strong repulsive electron-electron interactions at moderate values of the electron-phonon coupling. These spatially modulated charge clouds exhibit pairing with a typical length-scale set by the Fermi momentum.
The nonequilibrium effects of dissipation and drive play a key role in an immense variety of nanoscale and mesoscale quantum systems. To understand the behaviour of open quantum systems, we need accurate methods that capture the influence of the environment on the system, while managing the exponentially large Hilbert space required to describe the system. Tensor network algorithms offer an efficient way to approach this challenge. In this thesis, we develop and apply tensor network techniques to study the dynamics and steady states of various open quantum systems. The first part of the thesis focuses on the driven dissipative many body physics in coupled cavity arrays described by Born-Markov master equations. We extend transfer matrix product operator methods to Liouvillian dynamics, and utilize them to compute dynamical correlation functions and fluorescence spectrum of an infinite coupled cavity array in 1D. We also investigate thermalization, and observe the emergence of a quasi-thermal steady state with a negative effective temperature. In another study, we use infinite projected entangled pair state (iPEPS) methods to compute steady states of coupled cavity lattices in 2D. We find that a straightforward adaptation of iPEPS to Liouvillian dynamics is unstable, contradicting a recent publication in the field. The second part investigates more general systems involving strong couplings and structured environments that induce non-Markovian dynamics. We develop a powerful time-evolving matrix product operator (TEMPO) algorithm that builds on Feynman-Vernon influence functional formalism, and uses matrix product states (MPS) to represent the temporal non-Markovian correlations efficiently. We apply TEMPO to study the localization phase transition of the spin-boson model and the dynamics of two spatially separated two-level systems coupled to a common environment. Finally, we propose the Toblerone TEMPO algorithm, which extends TEMPO to many-body systems interacting with general bosonic environments.
We investigate the ground-state properties of the bipolaron coupled to quantum dispersive optical phonons in the one-dimensional Holstein-Hubbard model. We concentrate on the interplay between the phonon dispersion and the Coulomb repulsion and their mutual effect on the bipolaron effective mass, the binding energy, and the phase diagram. Most surprisingly, the sign of the curvature of the optical phonon dispersion plays a decisive role in the bipolaron binding energy in the presence of the Coulomb repulsion UUU. In particular, when the sign of the phonon dispersion curvature matches the sign of the electron dispersion curvature, the bipolaron remains bound in the strong-coupling limit even when $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and the binding emanates from the exchange of phonons between two electrons residing on adjacent sites. At moderate electron-phonon coupling a light bipolaron exists up to large values of UUU. Finally, an intuitive explanation of the role of the phonon dispersion on the bipolaron binding energy is derived using the strong-coupling limit where the binding emanates from the exchange of phonons between two electrons residing on adjacent sites which leads to enhanced stability of bipolarons at elevated Coulomb repulsion.
In this thesis, I investigate the transport and dynamical properties of electron-phonon coupled systems using numerical methods. I focus on the one-dimensional Holstein model, which incorporates both polaron and charge density wave (CDW) physics, and use matrix-product-state-based algorithms. In the first part, I present work where we combine purification with local basis optimization to study the finite-temperature properties of the model. This gives access to polaron spectral functions, polaron and bipolaron optical conductivity, and the energy-transport coefficient at finite filling. The second part focuses on the Holstein model coupled to two tight-binding leads. There, we investigate how current is transported through the structure and how CDW states break down. In the last part, we analyze the spread of an electron in a lattice and the decay of CDWs. We aim to understand if a full quantum mechanical treatment of the phonons is necessary or if trajectory-based algorithms are applicable.