We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, ${J}_{k}$ , to a two-dimensional electron gas. At weak ${J}_{k}$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large ${J}_{k}$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, ${J}_{k}$, to a two-dimensional electron gas. At weak ${J}_{k}$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large ${J}_{k}$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

arXiv:2204.00029Physical review. B./Physical review. BOct 4, 202218 citations

Saddle point solution of the Landau-Ginzburg-Wilson Hamiltonian for the McCoy-Wu Ising model

Xintian Wu

The Landau-Ginzburg-Wilson Hamiltonian for the McCoy-Wu strip-random Ising model on a two-dimensional lattice is studied. In the Landau-Ginzburg-Wilson Hamiltonian, the random temperature only depends on one of the coordinates ( $x$ ), the horizontal coordinate. The difference (rather than differential) saddle point equation is solved numerically. In the critical regime, there exist locally ordered regions, where the saddle point solutions are not zero. Due to the translational invariance in the vertical direction, the locally ordered regions are striplike in the vertical direction. In the excited state solutions, there exist horizontal domain walls across the locally ordered regions. It is found that these horizontal domain walls are stabilized by free-energy barriers due to the discreteness. The stability conditions for such domain walls are studied. Usually, the domain wall across multiple locally ordered regions can be stable. These multiple locally ordered regions form an elementary cluster. The criterion for multiple locally ordered regions forming an elementary cluster is obtained. At the saddle point level, we get an effective Hamiltonian in which the elementary clusters behave as Ising spins and are coupled with their neighbors. For the random temperatures with narrow uniform probability distributions, the distribution of elementary cluster size, the horizontal and vertical bonds between elementary clusters are calculated numerically. The vertical bonds are extremely strong and the horizontal bonds are extremely weak. The distribution of vertical bonds is exponential. There is an exponentially small probability of elementary clusters with extremely large size. These elementary clusters with extremely large size will cause the susceptibility divergent in a range of temperature. The random temperature with binary probability distributions is also studied. The qualitative properties are the same. The Griffiths-McCoy singularity in the saddle point solutions does not depend on the distribution of random temperature.The Landau-Ginzburg-Wilson Hamiltonian for the McCoy-Wu strip-random Ising model on a two-dimensional lattice is studied. In the Landau-Ginzburg-Wilson Hamiltonian, the random temperature only depends on one of the coordinates ($x$), the horizontal coordinate. The difference (rather than differential) saddle point equation is solved numerically. In the critical regime, there exist locally ordered regions, where the saddle point solutions are not zero. Due to the translational invariance in the vertical direction, the locally ordered regions are striplike in the vertical direction. In the excited state solutions, there exist horizontal domain walls across the locally ordered regions. It is found that these horizontal domain walls are stabilized by free-energy barriers due to the discreteness. The stability conditions for such domain walls are studied. Usually, the domain wall across multiple locally ordered regions can be stable. These multiple locally ordered regions form an elementary cluster. The criterion for multiple locally ordered regions forming an elementary cluster is obtained. At the saddle point level, we get an effective Hamiltonian in which the elementary clusters behave as Ising spins and are coupled with their neighbors. For the random temperatures with narrow uniform probability distributions, the distribution of elementary cluster size, the horizontal and vertical bonds between elementary clusters are calculated numerically. The vertical bonds are extremely strong and the horizontal bonds are extremely weak. The distribution of vertical bonds is exponential. There is an exponentially small probability of elementary clusters with extremely large size. These elementary clusters with extremely large size will cause the susceptibility divergent in a range of temperature. The random temperature with binary probability distributions is also studied. The qualitative properties are the same. The Griffiths-McCoy singularity in the saddle point solutions does not depend on the distribution of random temperature.

Physical review. B./Physical review. BJun 20, 20181 citation

Evidence for Landau Damping of Tonks-Dattner Resonances

R. W. Huggins, Manfred Raether

Physical Review LettersOct 3, 19667 citations

Dissipative Phenomena at Fermi Energies

A. Olmi

Jan 1, 19910 citations

Quantum critical metals in d=3+1 dimensions

Raghu Mahajan, David M. Ramirez, Shamit Kachru A +1 more

We study the problem of disorder-free metals in the vicinity of a quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the Yukawa coupling between the electrons and undamped bosons (order-parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale, however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the ``marginal Fermi liquid'' phenomenology [Varma et al., Phys. Rev. Lett. 63, 1996 (1989)]. We discuss a large- $N$ theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.We study the problem of disorder-free metals in the vicinity of a quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the Yukawa coupling between the electrons and undamped bosons (order-parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale, however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the ``marginal Fermi liquid'' phenomenology [Varma et al., Phys. Rev. Lett. 63, 1996 (1989)]. We discuss a large-$N$ theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.

arXiv:1303.1587Physical Review BSep 10, 201350 citations

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction,

{J}_{k}

, to a two-dimensional electron gas. At weak

{J}_{k}

the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large

{J}_{k}

Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

x

), the horizontal coordinate. The difference (rather than differential) saddle point equation is solved numerically. In the critical regime, there exist locally ordered regions, where the saddle point solutions are not zero. Due to the translational invariance in the vertical direction, the locally ordered regions are striplike in the vertical direction. In the excited state solutions, there exist horizontal domain walls across the locally ordered regions. It is found that these horizontal domain walls are stabilized by free-energy barriers due to the discreteness. The stability conditions for such domain walls are studied. Usually, the domain wall across multiple locally ordered regions can be stable. These multiple locally ordered regions form an elementary cluster. The criterion for multiple locally ordered regions forming an elementary cluster is obtained. At the saddle point level, we get an effective Hamiltonian in which the elementary clusters behave as Ising spins and are coupled with their neighbors. For the random temperatures with narrow uniform probability distributions, the distribution of elementary cluster size, the horizontal and vertical bonds between elementary clusters are calculated numerically. The vertical bonds are extremely strong and the horizontal bonds are extremely weak. The distribution of vertical bonds is exponential. There is an exponentially small probability of elementary clusters with extremely large size. These elementary clusters with extremely large size will cause the susceptibility divergent in a range of temperature. The random temperature with binary probability distributions is also studied. The qualitative properties are the same. The Griffiths-McCoy singularity in the saddle point solutions does not depend on the distribution of random temperature.

We study the problem of disorder-free metals in the vicinity of a quantum critical point in

d=3+1

dimensions. We begin with perturbation theory in the Yukawa coupling between the electrons and undamped bosons (order-parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale, however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the ``marginal Fermi liquid'' phenomenology [Varma et al., Phys. Rev. Lett. 63, 1996 (1989)]. We discuss a large-

N

theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.