Stability and bound states of molecules & Landau-Fermi liquid and instabilities

We study the effects of spin-antisymmetric interactions on the stability of a Landau–Fermi liquid on the square lattice, using the generalized Pomeranchuk method for two-dimensional lattice systems. In particular, we analyze interactions that could induce instabilities of the so-called spin-split type, that is when spin-up and spin-down Fermi surfaces are displaced with respect to each other. The phase space is studied as a function of the strength of the interaction V, the electron chemical potential μ and an external magnetic field h. We find that such interactions produce in general an enhancement of the instability region of the Landau–Fermi liquid. More interestingly, in certain regions of the V–μ phase space, we find a reentrant behavior as a function of the magnetic field h, similar to that found in recent experiments, e.g. in URu₂Si₂ and Sr₃Ru₂O₇.We study the effects of spin-antisymmetric interactions on the stability of a Landau–Fermi liquid on the square lattice, using the generalized Pomeranchuk method for two-dimensional lattice systems. In particular, we analyze interactions that could induce instabilities of the so-called spin-split type, that is when spin-up and spin-down Fermi surfaces are displaced with respect to each other. The phase space is studied as a function of the strength of the interaction V, the electron chemical potential μ and an external magnetic field h. We find that such interactions produce in general an enhancement of the instability region of the Landau–Fermi liquid. More interestingly, in certain regions of the V–μ phase space, we find a reentrant behavior as a function of the magnetic field h, similar to that found in recent experiments, e.g. in URu₂Si₂ and Sr₃Ru₂O₇.

Jan 1, 20122 citations

On the stability of a fermi liquid

I.Ya. Pomeranchuk

Jan 1, 195926 citations

Roton Fermi liquid: A metallic phase of two-dimensional electrons

Leon Balents, Matthew P. A. Fisher

We introduce and analyze a metallic phase of two-dimensional $(2\mathrm{D})$ electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of $2\mathrm{D}$ electrons consisting of fermionic quasiparticles and $hc∕2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$ , but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.We introduce and analyze a metallic phase of two-dimensional $(2\mathrm{D})$ electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of $2\mathrm{D}$ electrons consisting of fermionic quasiparticles and $hc∕2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.

arXiv:cond-mat/0307446Physical Review BFeb 28, 200513 citations

Landau Fermi-liquid theory

Piers Coleman

Cambridge University Press eBooksNov 26, 201518 citations

Correspondence between many-body localization and Landau–Fermi liquid of weakly interacting electrons and its normal-state instability in solids

Yiming Pan, Jinze He, Qiaofei Pan

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

We introduce and analyze a metallic phase of two-dimensional

(2\mathrm{D})

electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of

2\mathrm{D}

electrons consisting of fermionic quasiparticles and

hc∕2e

vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature

(T=0)

, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.