In quantum mechanics, the wavefunction of a free electron intrinsically embodies wave-particle duality, exhibiting wave- and (or) particle-like characteristics upon measurement. In solids, electrons depart from this idealized description; their low-energy excitations are quasiparticles that, within a single-particle perspective, govern material behavior. Here, we present a comparative analysis of the normal states within the many-body localization (MBL) and Landau-Fermi liquid (LFL) frameworks. We propose a phenomenological correspondence between LFL quasiparticles and the local integral of motion (LIOMs) in an MBL phase, which we term the MBL/LFL duality, by analogy to the wave-particle duality of an electron in free space. Within this heuristic framework, we argue that instabilities of an MBL 'normal state' can admit analogues of Fermi-liquid (FL) instabilities, such as LIOM pairing, and we outline both mean-field and renormalization-group perspectives that highlight possible routes to exotic nonequilibrium phases. These results are primarily suggestive: where small-scale numerical illustrations are presented, they serve to exemplify the proposed scenarios rather than constitute exhaustive numerical proof. Finally, our work offers a broader perspective in which MBL may represent not only a stable endpoint but also a setting for normal-state instabilities that parallel those of conventional Fermi liquids. We hope that the MBL/LFL duality can provide a new avenue for understanding exotic nonequilibrium phases that may emerge from the interplay between localization and interaction-driven instabilities.In quantum mechanics, the wavefunction of a free electron intrinsically embodies wave-particle duality, exhibiting wave- and (or) particle-like characteristics upon measurement. In solids, electrons depart from this idealized description; their low-energy excitations are quasiparticles that, within a single-particle perspective, govern material behavior. Here, we present a comparative analysis of the normal states within the many-body localization (MBL) and Landau-Fermi liquid (LFL) frameworks. We propose a phenomenological correspondence between LFL quasiparticles and the local integral of motion (LIOMs) in an MBL phase, which we term the MBL/LFL duality, by analogy to the wave-particle duality of an electron in free space. Within this heuristic framework, we argue that instabilities of an MBL 'normal state' can admit analogues of Fermi-liquid (FL) instabilities, such as LIOM pairing, and we outline both mean-field and renormalization-group perspectives that highlight possible routes to exotic nonequilibrium phases. These results are primarily suggestive: where small-scale numerical illustrations are presented, they serve to exemplify the proposed scenarios rather than constitute exhaustive numerical proof. Finally, our work offers a broader perspective in which MBL may represent not only a stable endpoint but also a setting for normal-state instabilities that parallel those of conventional Fermi liquids. We hope that the MBL/LFL duality can provide a new avenue for understanding exotic nonequilibrium phases that may emerge from the interplay between localization and interaction-driven instabilities.

Journal of Physics Condensed MatterFeb 3, 20260 citations

Quasiparticle picture of high-temperature superconductors in the frame of a Fermi liquid with the fermion condensate

M. Ya. Amusia, Vasily R. Shaginyan

A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses ${M}_{\mathrm{FC}}^{*}$ and ${M}_{L}^{*},$ respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses ${M}_{\mathrm{FC}}^{*}$ and ${M}_{L}^{*},$ respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].

arXiv:cond-mat/0102229Physical review. B, Condensed matterMay 21, 200131 citations

Quasi-particle properties in a quasi-two-dimensional electron liquid

Reza Asgari, B. Tanatar

PramanaFeb 1, 20080 citations

Quasi-particle properties in an electron-hole liquid

Thomas Maurice Rice

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BSep 1, 197472 citations

Marginal Fermi Liquid from a Partially Nested Fermi Surface and Impurity Scattering in a Two Dimensional Metal

Eliot Kapit

The electron-electron scattering rate of low-energy quasiparticles is computed perturbatively for a two-dimensional metal with a partially nested Fermi surface, a weak electron-electron interaction and an energy-independent impurity scattering rate. We show that even when the nested section comprises only a small fraction of the Fermi surface, the low energy quasiparticle decay rates throughout the Fermi surface gain a term which is linear in energy $ω$ . The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate $δ$ . We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.The electron-electron scattering rate of low-energy quasiparticles is computed perturbatively for a two-dimensional metal with a partially nested Fermi surface, a weak electron-electron interaction and an energy-independent impurity scattering rate. We show that even when the nested section comprises only a small fraction of the Fermi surface, the low energy quasiparticle decay rates throughout the Fermi surface gain a term which is linear in energy $ω$. The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate $δ$. We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.

arXiv:1103.6179Mar 31, 20110 citations

{M}_{\mathrm{FC}}^{*}

and

{M}_{L}^{*},

respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].

ω

. The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate

δ

. We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.