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Subir Sachdev - One of the best experts on this subject based on the ideXlab platform.
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spin density wave order topological order and Fermi surface reconstruction
Physical Review B, 2016Co-Authors: Subir Sachdev, Shubhayu Chatterjee, Erez Berg, Yoni SchattnerAbstract:In the conventional theory of density wave ordering in metals, the onset of spin density wave (SDW) order coincides with the reconstruction of the Fermi surfaces into small ``pockets.'' We present models which display this transition, while also displaying an alternative route between these phases via an intermediate phase with topological order, no broken symmetry, and pocket Fermi surfaces. The models involve coupling emergent gauge fields to a fractionalized SDW order, but retain the canonical electron operator in the underlying Hamiltonian. We establish an intimate connection between the suppression of certain defects in the SDW order and the presence of Fermi surface sizes distinct from the Luttinger value in Fermi Liquids. We discuss the relevance of such models to the physics of the hole-doped cuprates near optimal doping.
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the novel metallic states of the cuprates topological Fermi Liquids and strange metals
arXiv: Strongly Correlated Electrons, 2016Co-Authors: Subir Sachdev, Debanjan ChowdhuryAbstract:This article is based on a talk by S.S. at the Nambu Memorial Symposium at the University of Chicago. We review ideas on the nature of the metallic states of the hole-doped cuprate high temperature superconductors, with an emphasis on the connections between the Luttinger theorem for the size of the Fermi surface, topological quantum field theories (TQFTs), and critical theories involving changes in the size of the Fermi surface. We begin with the derivation of the Luttinger theorem for a Fermi liquid, using momentum balance during a process of flux-insertion in a lattice electronic model with toroidal boundary conditions. We then review the TQFT of the Z2 spin liquid, and demonstrate its compatibility with the toroidal momentum balance argument. This discussion leads naturally to a simple construction of `topological' Fermi liquid states: the fractionalized Fermi liquid (FL*) and the algebraic charge liquid (ACL). We present arguments for a description of the pseudogap metal of the cuprates using Z2-FL* or Z2-ACL states with Ising-nematic order. These pseudogap metal states are also described as Higgs phases of a SU(2) gauge theory. The Higgs field represents local antiferromagnetism, but the Higgs-condensed phase does not have long-range antiferromagnetic order: the magnitude of the Higgs field determines the pseudogap, the reconstruction of the Fermi surface, and the Ising-nematic order. Finally, we discuss the route to the large Fermi surface Fermi liquid via the critical point where the Higgs condensate and Ising nematic order vanish, and the application of Higgs criticality to the strange metal.
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transport near the ising nematic quantum critical point of metals in two dimensions
Physical Review B, 2014Co-Authors: Sean A Hartnoll, Raghu Mahajan, Matthias Punk, Subir SachdevAbstract:We consider two-dimensional metals near a Pomeranchuk instability which breaks ${90}^{\ensuremath{\circ}}$ lattice rotation symmetry. Such metals realize strongly coupled non-Fermi Liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation and, hence, a nonzero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the $d$-wave channel acts as a random ``field'' on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.
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weak magnetism and non Fermi Liquids near heavy Fermion critical points
Physical Review B, 2004Co-Authors: T Senthil, Matthias Vojta, Subir SachdevAbstract:This paper is concerned with the weak-moment magnetism in heavy-Fermion materials and its relation to the non-Fermi liquid physics observed near the transition to the Fermi liquid. We explore the hypothesis that the primary fluctuations responsible for the non-Fermi liquid physics are those associated with the destruction of the large Fermi surface of the Fermi liquid. Magnetism is suggested to be a low-energy instability of the resulting small Fermi surface state. A concrete realization of this picture is provided by a fractionalized Fermi liquid state which has a small Fermi surface of conduction electrons, but also has other exotic excitations with interactions described by a gauge theory in its deconfined phase. Of particular interest is a three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a U(1) gauge structure. A direct second-order transition from this state to the conventional Fermi liquid is possible and involves a jump in the electron Fermi surface volume. The critical point displays non-Fermi liquid behavior. A magnetic phase may develop from a spin density wave instability of the spinon Fermi surface. This exotic magnetic metal may have a weak ordered moment although the local moments do not participate in the Fermi surface. Experimental signatures of this phase and implications for heavy-Fermion systems are discussed.
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quantum phase transitions
2001Co-Authors: Subir SachdevAbstract:Part I. Introduction: 1. Basic concepts 2. The mapping to classical statistical mechanics: single site models 3. Overview Part II. Quantum Ising and Rotor Models: 4. The Ising chain in a transverse field 5. Quantum rotor models: large N limit 6. The d = 1, 0 (N greater than or equal to 3) rotor models 7. The d = 2 (N greater than or equal to 3) rotor models 8. Physics close to and above the upper-critical dimension 9. Transport in d = 2 Part III. Other Models: 10. Boston Hubbard model 11. Dilute Fermi and Bose gases 12. Phase transitions of Fermi Liquids 13. Heisenberg spins: ferromagnets and antiferromagnets 14. Spin chains: bosonization 15. Magnetic ordering transitions of disordered systems 16. Quantum spin glasses.
T Senthil - One of the best experts on this subject based on the ideXlab platform.
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mixed valence insulators with neutral Fermi surfaces
Nature Communications, 2018Co-Authors: Debanjan Chowdhury, Inti Sodemann, T SenthilAbstract:Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 K. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless Fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators—a composite exciton Fermi liquid—hosts a three dimensional Fermi surface of a neutral Fermion, that we name the “composite exciton.” We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi Liquids and make comparison to experiments in SmB6. Samarium hexaboride is a candidate topological insulator but recent experiments have found behaviour indicative of a metallic Fermi liquid phase. Here the authors show that the conflicting observations can be accommodated by a model where strong interactions drive the formation of exotic neutral quasiparticles.
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mixed valence insulators with neutral Fermi surfaces
arXiv: Strongly Correlated Electrons, 2017Co-Authors: Debanjan Chowdhury, Inti Sodemann, T SenthilAbstract:Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 kelvin. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless Fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators - composite exciton Fermi liquid - hosts a three dimensional Fermi surface of a neutral Fermion, that we name the "composite exciton". We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi Liquids and make comparison to experiments in SmB$_6$.
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composite Fermi Liquids in the lowest landau level
Physical Review B, 2016Co-Authors: Chong Wang, T SenthilAbstract:A quantum vortex liquid theory for composite Fermi liquid (CFL) states in the lowest Landau level is proposed. Contrary to the traditional Halperin-Lee-Read approach, the composite Fermions in this formulation are vortices carrying no physical charge. Furthermore, a Berry phase ${\ensuremath{\phi}}_{B}$=-2$\ensuremath{\pi}\phantom{\rule{0}{0ex}}\ensuremath{\nu}$ is enclosed by the composite Fermi surface, where $\ensuremath{\nu}$ is the total filling fraction. This vortex liquid theory is closely related to Read's formulation of bosonic CFL at $\ensuremath{\nu}=1$ in the 1990's, and to Son's recent formulation of the half-filled Landau level in terms of Dirac composite Fermions. Various consequences of this new picture are studied, including some nontrivial predictions for transport properties, and an emergent particle-hole symmetry for bosons at $\ensuremath{\nu}=1$.
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weak magnetism and non Fermi Liquids near heavy Fermion critical points
Physical Review B, 2004Co-Authors: T Senthil, Matthias Vojta, Subir SachdevAbstract:This paper is concerned with the weak-moment magnetism in heavy-Fermion materials and its relation to the non-Fermi liquid physics observed near the transition to the Fermi liquid. We explore the hypothesis that the primary fluctuations responsible for the non-Fermi liquid physics are those associated with the destruction of the large Fermi surface of the Fermi liquid. Magnetism is suggested to be a low-energy instability of the resulting small Fermi surface state. A concrete realization of this picture is provided by a fractionalized Fermi liquid state which has a small Fermi surface of conduction electrons, but also has other exotic excitations with interactions described by a gauge theory in its deconfined phase. Of particular interest is a three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a U(1) gauge structure. A direct second-order transition from this state to the conventional Fermi liquid is possible and involves a jump in the electron Fermi surface volume. The critical point displays non-Fermi liquid behavior. A magnetic phase may develop from a spin density wave instability of the spinon Fermi surface. This exotic magnetic metal may have a weak ordered moment although the local moments do not participate in the Fermi surface. Experimental signatures of this phase and implications for heavy-Fermion systems are discussed.
Senthil T. - One of the best experts on this subject based on the ideXlab platform.
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Non-Fermi Liquids as ersatz Fermi Liquids: general constraints on compressible metals
'American Physical Society (APS)', 2021Co-Authors: Else Dominic, Thorngren Ryan, Senthil T.Abstract:A system with charge conservation and lattice translation symmetry has a well-defined filling $\nu$, which is a real number representing the average charge per unit cell. We show that if $\nu$ is fractional (i.e. not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if $\nu$ is continuously tunable (i.e. the system is charge-compressible), in which case we show that the low-energy theory must have a very large emergent symmetry group -- larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi Liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an "ersatz Fermi liquid". We show that ersatz Fermi Liquids share a number of properties in common with Fermi Liquids, including Luttinger's theorem (which is thus extended to a large class of non-Fermi Liquids) and periodic "quantum oscillations" in the response to an applied magnetic field. We also establish versions of Luttinger's theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators. Our work makes connection between filling constraints and the theory of symmetry-protected topological (SPT) phases, in particular through the concept of " 't Hooft anomalies".Comment: 25 pages + 7 pages appendices. v4 Published versio
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Strange metals as ersatz Fermi Liquids
2021Co-Authors: Else Dominic, Senthil T.Abstract:A long standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature ($T$). In this paper we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency ($\omega$) dependent conductivity satisfies $\omega/T$ scaling, we argue that the $T$-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are `ersatz Fermi Liquids' with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion/time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes which necessarily imply other exotic phenomena.Comment: 6 pages + 4 pages appendices. v3 various minor correction
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Bose-Luttinger Liquids
2021Co-Authors: Lake Ethan, Senthil T., Vishwanath AshvinAbstract:We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub "Bose-Luttinger Liquids", which in some respects can be regarded as bosonic versions of Fermi Liquids, while in other respects exhibit striking differences. These phases have bosonic analogues of Fermi surfaces, and like Fermi Liquids they possess a large number of emergent conservation laws. Unlike Fermi Liquids however these phases lack quasiparticles, possess different RG flows, and have correlation functions controlled by a continuously varying exponent $\eta$, which characterizes the anomalous dimension of the bosonic field. We show that when $\eta>1$, these phases are stable with respect to all symmetric perturbations. These theories may be of relevance to several physical situations, including frustrated quantum magnets, rotons in superfluid He, and superconductors with finite-momentum pairing. As a concrete application, we show that coupling a Bose-Luttinger liquid to a conventional Fermi liquid produces a resistivity scaling with temperature as $T^\eta$. We argue that this may provide an explanation for the non-Fermi liquid resistivity observed in the paramagnetic phase of MnSi.Comment: 19+6 page
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Bose-Luttinger Liquids
2021Co-Authors: Lake Ethan, Senthil T., Vishwanath AshvinAbstract:We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub "Bose-Luttinger Liquids", which in some respects can be regarded as bosonic versions of Fermi Liquids, while in other respects exhibit striking differences. These phases have bosonic analogues of Fermi surfaces, and like Fermi Liquids they possess a large number of emergent conservation laws. Unlike Fermi Liquids however these phases lack quasiparticles, possess different RG flows, and have correlation functions controlled by a continuously varying exponent $\eta$, which characterizes the anomalous dimension of the bosonic field. We show that when $\eta>1$, these phases are stable with respect to all symmetric perturbations. These theories may be of relevance to several physical situations, including frustrated quantum magnets, rotons in superfluid He, and superconductors with finite-momentum pairing. As a concrete application, we show that coupling a Bose-Luttinger liquid to a conventional Fermi liquid produces a resistivity scaling with temperature as $T^\eta$. We argue that this may provide an explanation for the non-Fermi liquid resistivity observed in the paramagnetic phase of MnSi.Comment: 19+6 pages; updated references and minor edit
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Strange metals as ersatz Fermi Liquids
2020Co-Authors: Else Dominic, Senthil T.Abstract:A long standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature ($T$). In this paper we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency ($\omega$) dependent conductivity satisfies $\omega/T$ scaling, we argue that the $T$-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are `ersatz Fermi Liquids' with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion/time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes which necessarily imply other exotic phenomena.Comment: 7 pages + 2 pages appendices. v2 some clarifications and typos fixe
David Vegh - One of the best experts on this subject based on the ideXlab platform.
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Charge transport by holographic Fermi surfaces
Physical Review D, 2013Co-Authors: Thomas Faulkner, Hong Liu, John Mcgreevy, Nabil Iqbal, David VeghAbstract:For over fifty years our understanding of the lowtemperature properties of metals has been based on Laudau’s theory of Fermi Liquids. In Fermi liquid theory, the ground state of an interacting Fermionic system is characterized by a Fermi surface in momentum space, and the low energy excitations are weakly interacting Fermionic quasiparticles near the Fermi surface. This picture of well-defined quasiparticles close to the Fermi surface provides a powerful tool for obtaining low temperature properties of the system and has been very successful in explaining most metallic states observed in nature, from liquid 3 He to heavy Fermion behavior in rare earth compounds.
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non Fermi Liquids from holography
Physical Review D, 2011Co-Authors: Hong Liu, John Mcgreevy, David VeghAbstract:We report on a potentially new class of non-Fermi Liquids in (2+1)-dimensions. They are identified via the response functions of composite Fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless Fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.
Yizhi You - One of the best experts on this subject based on the ideXlab platform.
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nematic quantum phase transition of composite Fermi Liquids in half filled landau levels and their geometric response
Physical Review B, 2016Co-Authors: Yizhi You, Gil Young Cho, Eduardo FradkinAbstract:We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi Liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure, which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite Fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective-field theory for the isotropic-nematic phase transition is shown to have $z=3$ dynamical exponent due to the Landau damping of the dense Fermi system. We show that there is a Berry-phase-type term that governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a nonuniversal ``Hall viscosity'' of the dynamical metric. We also show that the effective-field theory of this compressible fluid has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative (one-loop) computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the topological excitation of the nematic fluid, the disclination, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.