SU($\boldsymbol N$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order
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arXiv
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2024
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| _version_ | 1866910463701286912 |
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| author | Raczkowski, Marcin Assaad, Fakher F. |
| author_facet | Raczkowski, Marcin Assaad, Fakher F. |
| contents | We map out the ground state phase diagram of a one-dimensional SU($N$) Kondo-Heisenberg lattice model at half filling and in the fully antisymmetric self-adjoint representation as a function of $\tfrac {1}{N}$ 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 SU($N\ge 4$) 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 $N\to\infty$ 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 SU($N$) symmetry and low dimensionality of the RKKY exchange interaction are not sufficient to induce VBS order in the conventional SU($N$) Kondo chain which hosts solely a KI phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SU($\boldsymbol N$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order Raczkowski, Marcin Assaad, Fakher F. Strongly Correlated Electrons We map out the ground state phase diagram of a one-dimensional SU($N$) Kondo-Heisenberg lattice model at half filling and in the fully antisymmetric self-adjoint representation as a function of $\tfrac {1}{N}$ 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 SU($N\ge 4$) 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 $N\to\infty$ 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 SU($N$) symmetry and low dimensionality of the RKKY exchange interaction are not sufficient to induce VBS order in the conventional SU($N$) Kondo chain which hosts solely a KI phase. |
| title | SU($\boldsymbol N$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.03694 |