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

Bulletin of the American Physical Society

Pseudogap temperature along the Widom line of a first-order transition in doped Mott insulators

G. Sordi, P. Sémon, Kristjan Haule, A.–M. S. Tremblay

Published Oct 6, 2011• 0 citations
OpenAlex

Abstract

The phase diagram of hole-doped high-temperature superconductors remains puzzling. A state of matter with unusual physical properties, dubbed pseudogap, is found below a characteristic temperature $T^*$ in a doped Mott insulator. Since the superconducting state is born out of the pseudogap over much of the phase diagram, the nature of the pseudogap is a fundamental issue in the field and it is under intense theoretical and experimental scrutiny. In many cases, it is not even clear whether $T^*$ is a crossover or a phase transition. Here we show, by constructing the normal-state phase diagram of the archetypal model of strongly correlated electron systems, that $T^*$ is a crossover line above a critical endpoint, while below that point it is a first-order phase transition between two metallic phases, one with a pseudogap and one without. Thus $T^*$ appears in a new light: it is an unexpected example of a phenomenon observed in fluids, namely a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. Our findings thus suggest that the critical point of a first-order transition can be the organizing principle for the rich behavior of the normal state of the cuprates.

Related papers

Pseudogap temperature as a Widom line in doped Mott insulators

G. Sordi, P. Sémon, Kristjan Haule +1 more

The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature T* in hole-doped high-temperature superconductors. Determining T* is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature T* is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.

arXiv:1110.1392•Scientific Reports•Jul 31, 2012•102 citations

Frenkel line and the pseudogap: An analogy between classical and electronic fluids

Jérôme Fournier, P.-O. Downey, Olivier Gingras +3 more

Asymptotically close to critical end points of first-order transitions, maxima in thermodynamic quantities occur along a line called the Widom line, a concept first introduced in classical fluids. This concept has been extended to strongly correlated electronic fluids in the context of the Mott transition. Namely, upon increasing interaction strength in the Hubbard model at half filling, one finds a first-order Mott metal-insulator transition with a critical end point at high temperature, above which several crossover lines are observable. Using the dynamical cluster approximation for the triangular-lattice Hubbard model, we compute the Frenkel line, a concept borrowed from classical fluids, which is used to define a sharp crossover between the pseudogap and the correlated Fermi liquid. The Frenkel line in the electron fluid is defined by the appearance of backscattering upon entering the pseudogap. The signature of backscattering is the existence of a negative value in the time-domain optical conductivity. The Frenkel line extends to high temperatures.

arXiv:2509.18317•Physical Review Research•May 12, 2026•0 citations

An organizing principle for two-dimensional strongly correlated superconductivity

Lorenzo Fratino, P. Sémon, G. Sordi +1 more

Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature Tc(d), the maximum of the condensation energy as a function of doping, the correlation between maximum Tc(D) and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

arXiv:1602.02278•Scientific Reports•Mar 11, 2016•72 citations

Strong Coupling Superconductivity, Pseudogap, and Mott Transition

G. Sordi, P. Sémon, Kristjan Haule +1 more

An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

arXiv:1201.1283•Physical Review Letters•May 23, 2012•159 citations

Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model

G. Sordi, Kristjan Haule, A.–M. S. Tremblay

For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength $U$, temperature $T$, and filling $n$ shows that, upon increasing $n$ toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T $=$ 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.

arXiv:1102.0463•Physical Review B•Aug 17, 2011•93 citations

Finite-temperature crossover and the quantum Widom line near the Mott transition

J. Vučičević, Hanna Terletska, D. Tanasković +1 more

The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high-temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of quantum Widom lines and present a detailed discussion that highlights its physical meaning when used in the context of quantum-phase transitions.

arXiv:1210.7201•Physical Review B•Aug 28, 2013•101 citations
The phase diagram of hole-doped high-temperature superconductors remains puzzling. A state of matter with unusual physical properties, dubbed pseudogap, is found below a characteristic temperature T∗T^*T∗ in a doped Mott insulator. Since the superconducting state is born out of the pseudogap over much of the phase diagram, the nature of the pseudogap is a fundamental issue in the field and it is under intense theoretical and experimental scrutiny. In many cases, it is not even clear whether T∗T^*T∗ is a crossover or a phase transition. Here we show, by constructing the normal-state phase diagram of the archetypal model of strongly correlated electron systems, that T∗T^*T∗ is a crossover line above a critical endpoint, while below that point it is a first-order phase transition between two metallic phases, one with a pseudogap and one without. Thus T∗T^*T∗ appears in a new light: it is an unexpected example of a phenomenon observed in fluids, namely a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. Our findings thus suggest that the critical point of a first-order transition can be the organizing principle for the rich behavior of the normal state of the cuprates.
The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature T* in hole-doped high-temperature superconductors. Determining T* is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature T* is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.
Asymptotically close to critical end points of first-order transitions, maxima in thermodynamic quantities occur along a line called the Widom line, a concept first introduced in classical fluids. This concept has been extended to strongly correlated electronic fluids in the context of the Mott transition. Namely, upon increasing interaction strength in the Hubbard model at half filling, one finds a first-order Mott metal-insulator transition with a critical end point at high temperature, above which several crossover lines are observable. Using the dynamical cluster approximation for the triangular-lattice Hubbard model, we compute the Frenkel line, a concept borrowed from classical fluids, which is used to define a sharp crossover between the pseudogap and the correlated Fermi liquid. The Frenkel line in the electron fluid is defined by the appearance of backscattering upon entering the pseudogap. The signature of backscattering is the existence of a negative value in the time-domain optical conductivity. The Frenkel line extends to high temperatures.
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature Tc(d), the maximum of the condensation energy as a function of doping, the correlation between maximum Tc(D) and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.
An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength UUU, temperature TTT, and filling nnn shows that, upon increasing nnn toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T === 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.
The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high-temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of quantum Widom lines and present a detailed discussion that highlights its physical meaning when used in the context of quantum-phase transitions.