We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional $d$ -wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasiextended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional $d$-wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasiextended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.

arXiv:1711.11540Physical review. B./Physical review. BApr 16, 20189 citations

Specific heat of a one-dimensional interacting Fermi system

Andrey V. Chubukov, Dmitrr Maslov, Ronojoy Saha

Bulletin of the American Physical SocietyMar 10, 20080 citations

Self-consistent random-phase approximation for hot finite Fermi systems

A.I. Vdovin, Daniel S. Kosov, W. Nawrocka

Theoretical and Mathematical PhysicsMay 1, 19972 citations

Specific heat of the Gaussian random bond Ising model on a square lattice

Olga V. Dimitrova

The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion and analysis of continuation of the high-temperature series. At low temperatures the specific heat follows the power law $C\propto T^{3/2}$ , the result confirmed independently by counting many-body states in finite size samples. The interpretation of the free energy in terms of independent droplet excitations gives the density of the two-level states, that follows a novel power law $\rho(\epsilon)\propto \sqrt{\epsilon}$ at low energies.The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion and analysis of continuation of the high-temperature series. At low temperatures the specific heat follows the power law $C\propto T^{3/2}$, the result confirmed independently by counting many-body states in finite size samples. The interpretation of the free energy in terms of independent droplet excitations gives the density of the two-level states, that follows a novel power law $\rho(\epsilon)\propto \sqrt{\epsilon}$ at low energies.

arXiv:1104.0037Mar 31, 20110 citations

A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

Hui-yi Tang, Jian-Hui Wang, Yongli Ma

For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann–Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis’s q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system–bath heat exchange and “uncompensated heat” which are in the thermodynamical level and independent on the detail of the system–bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann–Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis’s q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system–bath heat exchange and “uncompensated heat” which are in the thermodynamical level and independent on the detail of the system–bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.

Journal of the Physical Society of JapanMay 14, 20145 citations

Specific heat of the two-dimensional random Ising models

Makoto Inoue, 井上真

Jan 1, 19950 citations

We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional

d

-wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasiextended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.

C\propto T^{3/2}

, the result confirmed independently by counting many-body states in finite size samples. The interpretation of the free energy in terms of independent droplet excitations gives the density of the two-level states, that follows a novel power law

\rho(\epsilon)\propto \sqrt{\epsilon}

at low energies.