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Staggered liquid phases of the 1D Kondo-Heisenberg lattice model

Zachar, Oron

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

We introduce a new family of one dimensional liquids, which we label as \'\'Staggered-Liquids\'\', in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin gapped liquids and a new Luttinger liquid phase. A Staggered Liquid is characterized by gapless modes with \'\'large fermi-sea\'\' signature in the charge density wave (CDW) mode, and in that the superconducting order involves the near condensation of charge-2e Cooper pairs with finite center of mass momentum. In particular, the conventional gapless $2k_{F}$ CDW and $k=0$ pairing modes are absent. In the process, we analytically derive the phase transition from an intermediate coupling spin gap phase to the strong coupling gapless LL phase of the Kondo-Heisenberg lattice model.

Related papers

Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model

Oron Zachar

We describe a family of one-dimensional (1D) liquids, which we call ``staggered liquids,'' in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin-gapped liquids and a Luttinger liquid (LL) phase. A staggered liquid is characterized by gapless modes with a large Fermi-sea signature in the charge-density wave (CDW) mode, and the superconducting order involves the near condensation of charge-$2e$ Cooper pairs with finite center-of-mass momentum. In particular, the conventional gapless ${2k}_{F}$ CDW and $k=0$ pairing modes are absent. We analytically derive the phase transition from an intermediate-coupling spin-gap phase to the strong-coupling gapless LL phase of the Kondo-Heisenberg lattice model.

arXiv:cond-mat/0011312•Physical review. B, Condensed matter•Apr 13, 2001•38 citations

Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in a frustrated Kondo lattice

Jialin Chen, Jiangfan Wang, Yi‐feng Yang

Motivated by the recent discovery of an intermediate quantum critical phase between the antiferromagnetic order and the Fermi liquid in the frustrated Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ XXZ interactions among local spins using the density matrix renormalization group method. Our simulations reveal a global phase diagram with rich ground states including the antiferromagnetic order, the valence-bond-solid and bond-order-wave orders, the pair density wave state, the uniform superconducting state, and the Luttinger liquid state. We show that both the pair density wave and uniform superconductivity belong to the family of Luther-Emery liquids and may arise from pair instability of an intermediate quantum critical phase with medium Fermi volume in the presence of strong quantum fluctuations, while the Luttinger liquid has a large Fermi volume. Our work provides a comprehensive picture of the frustrated Kondo lattice physics at one dimension, and suggests a deep connection between the pair density wave, the unconventional superconductivity, and the non-Fermi liquid quantum critical phase.

arXiv:2308.11414•Physical review. B./Physical review. B•Jan 10, 2024•9 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

Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field

H. P. Zhang, Z. Song

We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.

arXiv:2609.29728•Sep 24, 2026•0 citations

Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Alexander Nikolaenko, Ya-Hui Zhang

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_K J K at fixed doping x. At large positive J_K J K , we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2} 2 k F = 1 + x 2 (in units of 2\pi 2 π ), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0 J K ≤ 0 side, our simulation finds the existence of a fractional Luttinger liquid (LL \star ⋆ ) phase with 2k_F=\frac{x}{2} 2 k F = x 2 , accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL \star ⋆ ) phase in higher dimensions. The LL \star ⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_K J K . Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_K J K , the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J 0.035 J ) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+ z = + . The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

arXiv:2306.09402•SciPost Physics•Aug 5, 2024•2 citations

Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain

A. Dobry, Akbar Jaefari, Eduardo Fradkin

We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-$\frac{1}{2}$ Luttinger liquid coupled by a Kondo exchange interaction ${J}_{K}$ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling ${J}_{1}$ and a next-nearest-neighbor (frustrating) exchange interaction ${J}_{2}$. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling ${J}_{K}$ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios ${J}_{K}/{J}_{1}$, ${J}_{2}/{J}_{1}$, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.

arXiv:1304.5256•Physical Review B•Jun 7, 2013•8 citations
We introduce a new family of one dimensional liquids, which we label as ''Staggered-Liquids'', in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin gapped liquids and a new Luttinger liquid phase. A Staggered Liquid is characterized by gapless modes with ''large fermi-sea'' signature in the charge density wave (CDW) mode, and in that the superconducting order involves the near condensation of charge-2e Cooper pairs with finite center of mass momentum. In particular, the conventional gapless 2kF2k_{F}2kF​ CDW and k=0k=0k=0 pairing modes are absent. In the process, we analytically derive the phase transition from an intermediate coupling spin gap phase to the strong coupling gapless LL phase of the Kondo-Heisenberg lattice model.
We describe a family of one-dimensional (1D) liquids, which we call ``staggered liquids,'' in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin-gapped liquids and a Luttinger liquid (LL) phase. A staggered liquid is characterized by gapless modes with a large Fermi-sea signature in the charge-density wave (CDW) mode, and the superconducting order involves the near condensation of charge-2e2e2e Cooper pairs with finite center-of-mass momentum. In particular, the conventional gapless 2kF{2k}_{F}2kF​ CDW and k=0k=0k=0 pairing modes are absent. We analytically derive the phase transition from an intermediate-coupling spin-gap phase to the strong-coupling gapless LL phase of the Kondo-Heisenberg lattice model.
Motivated by the recent discovery of an intermediate quantum critical phase between the antiferromagnetic order and the Fermi liquid in the frustrated Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ XXZ interactions among local spins using the density matrix renormalization group method. Our simulations reveal a global phase diagram with rich ground states including the antiferromagnetic order, the valence-bond-solid and bond-order-wave orders, the pair density wave state, the uniform superconducting state, and the Luttinger liquid state. We show that both the pair density wave and uniform superconductivity belong to the family of Luther-Emery liquids and may arise from pair instability of an intermediate quantum critical phase with medium Fermi volume in the presence of strong quantum fluctuations, while the Luttinger liquid has a large Fermi volume. Our work provides a comprehensive picture of the frustrated Kondo lattice physics at one dimension, and suggests a deep connection between the pair density wave, the unconventional superconductivity, and the non-Fermi liquid quantum critical phase.
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.
We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.
Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_K J K at fixed doping x. At large positive J_K J K , we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2} 2 k F = 1 + x 2 (in units of 2\pi 2 π ), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0 J K ≤ 0 side, our simulation finds the existence of a fractional Luttinger liquid (LL \star ⋆ ) phase with 2k_F=\frac{x}{2} 2 k F = x 2 , accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL \star ⋆ ) phase in higher dimensions. The LL \star ⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_K J K . Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_K J K , the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J 0.035 J ) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+ z = + . The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.