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:2403.03694 · Physical review. B./Physical review. B

SU ( N ) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order

Marcin Raczkowski, Fakher F. Assaad

Published May 29, 2024• 4 citations
arXivHTMLPDF

Abstract

We map out the ground-state phase diagram of a one-dimensional $\mathrm{SU}(N)$ Kondo-Heisenberg lattice model at half-filling and in the fully antisymmetric self-adjoint representation as a function of $\frac{1}{N}$ and Kondo coupling ${J}_{k}/t$. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even $N$ up to 8, we show that the enlarged $\mathrm{SU}(N\ensuremath{\ge}4$) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak-coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong ${J}_{k}/t$ limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing ${J}_{k}/t$, we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized $f$ spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-$N$ approximation, and we show that in the limit of infinite degeneracy $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized $f$ spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling ${J}_{h}=0$, and we provide evidence that the enlarged $\mathrm{SU}(N)$ symmetry and low dimensionality of the Ruderman-Kittel-Kasuya-Yosida exchange interaction are not sufficient to induce VBS order in the conventional $\mathrm{SU}(N)$ Kondo chain, which hosts solely a KI phase. Finally, we quantify the role of increasing $N$ in reducing the separation of charge and spin timescales specific to the KI state, and we show that the latter is adiabatically connected to a trivial band insulator captured by the large-$N$ approximation.

DOI
10.1103/physrevb.109.205154

Related papers

Zooming in on heavy fermions in Kondo lattice models

Bimla Danu, Zihong Liu, Fakher F. Assaad +1 more

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that, for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as ${e}^{\ensuremath{-}W/{J}_{k}}$ with $W$ the bandwidth and ${J}_{k}$ the Kondo coupling, the residue of the composite fermion tracks ${J}_{k}$. This result holds down to ${J}_{k}/W=0.05$ and confirms the point of view that magnetic ordering, present below ${J}_{k}/W=0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for $\mathrm{SU}(N)$ generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large ${J}_{k}$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.

arXiv:2107.10272•Physical review. B./Physical review. B•Oct 19, 2021•25 citations

Quantum critical point in the Kondo-Heisenberg model on the honeycomb lattice

Saeed Saremi, Patrick A. Lee

We study the Kondo-Heisenberg model on the honeycomb lattice at half filling. Due to the vanishing of the density of states at the fermi level, the Kondo insulator disappears at a finite Kondo coupling even in the absence of the Heisenberg exchange. We adopt a large-$N$ formulation of this model and use the renormalization group machinery to study systematically the second order phase transition of the Kondo insulator (KI) to the algebraic spin liquid (ASL). We note that neither phase breaks any physical symmetry, so that the transition is not described by the standard Ginzburg-Landau-Wilson critical point. We find a stable Lorentz-invariant fixed point that controls this second order phase transition. We calculate the exponent $\ensuremath{\nu}$ of the diverging length scale near the transition. The quasiparticle weight of the conduction electron vanishes at this KI-ASL fixed point, indicating non-Fermi-liquid behavior. The algebraic decay exponent of the staggered spin correlation is calculated at the fixed point and in the ASL phase. We find a jump in this exponent at the transition point.

arXiv:cond-mat/0610273•Physical Review B•Apr 17, 2007•27 citations

Phase diagram of the half-filled two-dimensional SU ( N ) Hubbard-Heisenberg model: A quantum Monte Carlo study

Fakher F. Assaad

We investigate the phase diagram of the half-filled $\mathrm{SU}(N)$ Hubbard-Heisenberg model with hopping $t$, exchange $J$, and Hubbard $U$, on a two-dimensional square lattice. In the large-$N$ limit, and as a function of decreasing values of $t∕J$, the model shows a transition from a $d$-density wave state to a spin dimerized insulator. A similar behavior is observed at $N=6$ whereas at $N=2$ a spin density wave insulating ground state is stabilized. The $N=4$ model, has a $d$-density wave ground state at large values of $t∕J$ which as a function of decreasing values of $t∕J$ becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power law, resulting in gapless spin excitations at $\stackrel{P\vec}{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors $\stackrel{P\vec}{q}=(0,\ensuremath{\pi})$ and $\stackrel{P\vec}{q}=(\ensuremath{\pi},0)$. This gapless spin liquid state is equally found in the SU(4) Heisenberg $(U∕t\ensuremath{\rightarrow}\ensuremath{\infty})$ model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a $\ensuremath{\pi}$-flux phase is offered. Our results stem from projective $(T=0)$ quantum Monte Carlo simulations on lattice sizes ranging up to $24\ifmmode\times\else\texttimes\fi{}24$.

arXiv:cond-mat/0406074•Physical Review B•Feb 4, 2005•139 citations

Spin correlations in dense Kondo systems

Paolo Maria Santini, Jenő Sólyom, Lucio Claudio Andreani +1 more

We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.

Journal of Applied Physics•May 15, 1993•1 citation

Magnetic quantum phase transition in a metallic Kondo heterostructure

Zi Hong Liu, Bernhard Frank, Lukas Janssen +2 more

We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.

arXiv:2211.02071•Physical review. B./Physical review. B•Apr 4, 2023•6 citations

Hubbard and Kondo lattice models in two dimensions : a QMC study

M. Feldbacher

This thesis discusses mainly two Fermionic lattice systems, first a Kondo lattice with additional Hubbard interaction and second a Hubbard Hamiltonian augmented with additional spin and charge interactions. We first introduce the Quantum Monte Carlo technique, which is then employed to study the two respective systems. We present an innovation that allows to calculate time displaced Greens functions more efficiently. Compared with previously used numerically stable algorithms the new method gains an order of magnitude in speed, but is just as precise, and very simple to implement. In the second chapter we consider the Kondo lattice model in two dimensions at half filling. In addition to the Fermionic hopping integral t and the superexchange coupling J the role of a Coulomb repulsion U in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of Jc which is decreasing as a function of U. The single-particle spectral function A(k,ω) is computed across this transition. We conclude that (i) the local screening of impurity spins determines the low-energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the half-filled Hubbard model at J=0 to that of the Kondo insulator at J>Jc. In the third chapter we investigate the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.

•Jan 1, 2003•0 citations
We map out the ground-state phase diagram of a one-dimensional SU(N)\mathrm{SU}(N)SU(N) Kondo-Heisenberg lattice model at half-filling and in the fully antisymmetric self-adjoint representation as a function of 1N\frac{1}{N}N1​ and Kondo coupling Jk/t{J}_{k}/tJk​/t. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even NNN up to 8, we show that the enlarged SU(N\ensuremath≥4\mathrm{SU}(N\ensuremath{\ge}4SU(N\ensuremath≥4) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak-coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong Jk/t{J}_{k}/tJk​/t limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing Jk/t{J}_{k}/tJk​/t, we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized fff spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-NNN approximation, and we show that in the limit of infinite degeneracy N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized fff spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling Jh=0{J}_{h}=0Jh​=0, and we provide evidence that the enlarged SU(N)\mathrm{SU}(N)SU(N) symmetry and low dimensionality of the Ruderman-Kittel-Kasuya-Yosida exchange interaction are not sufficient to induce VBS order in the conventional SU(N)\mathrm{SU}(N)SU(N) Kondo chain, which hosts solely a KI phase. Finally, we quantify the role of increasing NNN in reducing the separation of charge and spin timescales specific to the KI state, and we show that the latter is adiabatically connected to a trivial band insulator captured by the large-NNN approximation.
Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that, for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as ${e}^{\ensuremath{-}W/{J}_{k}}$ with WWW the bandwidth and Jk{J}_{k}Jk​ the Kondo coupling, the residue of the composite fermion tracks Jk{J}_{k}Jk​. This result holds down to Jk/W=0.05{J}_{k}/W=0.05Jk​/W=0.05 and confirms the point of view that magnetic ordering, present below Jk/W=0.18{J}_{k}/W=0.18Jk​/W=0.18, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for SU(N)\mathrm{SU}(N)SU(N) generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-NNN, large-SSS, and large Jk{J}_{k}Jk​. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.
We study the Kondo-Heisenberg model on the honeycomb lattice at half filling. Due to the vanishing of the density of states at the fermi level, the Kondo insulator disappears at a finite Kondo coupling even in the absence of the Heisenberg exchange. We adopt a large-NNN formulation of this model and use the renormalization group machinery to study systematically the second order phase transition of the Kondo insulator (KI) to the algebraic spin liquid (ASL). We note that neither phase breaks any physical symmetry, so that the transition is not described by the standard Ginzburg-Landau-Wilson critical point. We find a stable Lorentz-invariant fixed point that controls this second order phase transition. We calculate the exponent $\ensuremath{\nu}$ of the diverging length scale near the transition. The quasiparticle weight of the conduction electron vanishes at this KI-ASL fixed point, indicating non-Fermi-liquid behavior. The algebraic decay exponent of the staggered spin correlation is calculated at the fixed point and in the ASL phase. We find a jump in this exponent at the transition point.
We investigate the phase diagram of the half-filled SU(N)\mathrm{SU}(N)SU(N) Hubbard-Heisenberg model with hopping ttt, exchange JJJ, and Hubbard UUU, on a two-dimensional square lattice. In the large-NNN limit, and as a function of decreasing values of t∕Jt∕Jt∕J, the model shows a transition from a ddd-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6N=6N=6 whereas at N=2N=2N=2 a spin density wave insulating ground state is stabilized. The N=4N=4N=4 model, has a ddd-density wave ground state at large values of t∕Jt∕Jt∕J which as a function of decreasing values of t∕Jt∕Jt∕J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power law, resulting in gapless spin excitations at $\stackrel{P\vec}{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors $\stackrel{P\vec}{q}=(0,\ensuremath{\pi})$ and $\stackrel{P\vec}{q}=(\ensuremath{\pi},0)$. This gapless spin liquid state is equally found in the SU(4) Heisenberg $(U∕t\ensuremath{\rightarrow}\ensuremath{\infty})$ model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a $\ensuremath{\pi}$-flux phase is offered. Our results stem from projective (T=0)(T=0)(T=0) quantum Monte Carlo simulations on lattice sizes ranging up to $24\ifmmode\times\else\texttimes\fi{}24$.
We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.
We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.
This thesis discusses mainly two Fermionic lattice systems, first a Kondo lattice with additional Hubbard interaction and second a Hubbard Hamiltonian augmented with additional spin and charge interactions. We first introduce the Quantum Monte Carlo technique, which is then employed to study the two respective systems. We present an innovation that allows to calculate time displaced Greens functions more efficiently. Compared with previously used numerically stable algorithms the new method gains an order of magnitude in speed, but is just as precise, and very simple to implement. In the second chapter we consider the Kondo lattice model in two dimensions at half filling. In addition to the Fermionic hopping integral t and the superexchange coupling J the role of a Coulomb repulsion U in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of Jc which is decreasing as a function of U. The single-particle spectral function A(k,ω) is computed across this transition. We conclude that (i) the local screening of impurity spins determines the low-energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the half-filled Hubbard model at J=0 to that of the Kondo insulator at J>Jc. In the third chapter we investigate the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.