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

arXiv:cond-mat/0611536

Fermi surface change across a deconfined quantum critical point

Ribhu K. Kaul, Alexei K. Kolezhuk, Michael Levin, Subir Sachdev A, T. Senthil

Published Nov 20, 2006• 0 citations
arXivHTMLPDF

Abstract

The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.

DOI
10.48550/arxiv.cond-mat/0611536

Related papers

Hole dynamics in an antiferromagnet across a deconfined quantum critical point

Ribhu K. Kaul, Alexei K. Kolezhuk, Michael Levin +2 more

We study the effects of a small density of holes, $\ensuremath{\delta}$, on a square-lattice antiferromagnet undergoing a continuous transition from a N\'eel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero $\ensuremath{\delta}$, it is likely that the critical point broadens into a non-Fermi-liquid ``holon-metal'' phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio ${\mathrm{lim}}_{\ensuremath{\delta}\ensuremath{\rightarrow}0}{\mathcal{A}}_{F}∕\ensuremath{\delta}$ (where ${\mathcal{A}}_{F}$ is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at $\ensuremath{\delta}>0$, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as $\ensuremath{\delta}\ensuremath{\rightarrow}0$. We demonstrate that the electronic spectrum at the $\ensuremath{\delta}\ensuremath{\rightarrow}0$ transition is described by the ``boundary'' critical theory of an impurity coupled to a $(2+1)$-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble ``Fermi arc'' spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.

arXiv:cond-mat/0702119•Physical Review B•Jun 26, 2007•64 citations

Lectures on the quantum phase transitions of metals

Subir Sachdev A

Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.

arXiv:2407.15919•Jul 22, 2024•1 citation

Deconfined quantum criticality in the two-dimensional Kondo lattice model

Ki‐Seok Kim

We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.

arXiv:cond-mat/0505230•Physical Review B•Oct 28, 2005•4 citations

Stripe melting and quantum criticality in correlated metals

David F. Mross, T. Senthil

We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as ``stripe loop metals'' where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.

arXiv:1207.1442•Physical Review B•Sep 27, 2012•23 citations

Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model

Eitan Eidelstein, S. Moukouri, Avraham Schiller

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.

arXiv:1102.2573•Physical Review B•Jul 22, 2011•13 citations

Deconfined Fermi liquid to Fermi liquid transition and superconducting instability

Xiaofan Wu, Hui Yang, Ya-Hui Zhang

Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling ${J}_{\ensuremath{\perp}}$. Across the transition the Fermi-surface volume per flavor jumps by $1/2$ of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high ${T}_{\text{c}}$ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ and future experiments in bilayer optical lattice.

arXiv:2401.08753•Physical review. B./Physical review. B•Sep 10, 2024•10 citations
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.
We study the effects of a small density of holes, $\ensuremath{\delta}$, on a square-lattice antiferromagnet undergoing a continuous transition from a N\'eel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero $\ensuremath{\delta}$, it is likely that the critical point broadens into a non-Fermi-liquid ``holon-metal'' phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio ${\mathrm{lim}}_{\ensuremath{\delta}\ensuremath{\rightarrow}0}{\mathcal{A}}_{F}∕\ensuremath{\delta}$ (where AF{\mathcal{A}}_{F}AF​ is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at $\ensuremath{\delta}>0$, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as $\ensuremath{\delta}\ensuremath{\rightarrow}0$. We demonstrate that the electronic spectrum at the $\ensuremath{\delta}\ensuremath{\rightarrow}0$ transition is described by the ``boundary'' critical theory of an impurity coupled to a (2+1)(2+1)(2+1)-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble ``Fermi arc'' spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.
Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as ``stripe loop metals'' where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling ${J}_{\ensuremath{\perp}}$. Across the transition the Fermi-surface volume per flavor jumps by 1/21/21/2 of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high Tc{T}_{\text{c}}Tc​ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and future experiments in bilayer optical lattice.