J. Von Delft - Academia.edu (original) (raw)

Papers by J. Von Delft

We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ri... more We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we re-cently predicted a crossover for the dephasing time τϕ(T) from diffusive or ergodic 1D (τ−1ϕ ∝ T 2/3, T 1) to 0D behavior (τ−1ϕ ∝ T 2) as T drops below the Thouless energy ETh. 1 We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the 0D regime on equal foot-ing as the others. The crossover to 0D, predicted by Sivan, Imry and Aronov for 3D systems,2 has so far eluded experimental observation. We will show that for T ETh, 0D dephasing governs not only the T-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which re-sult only ...

Physical Review Letters

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, b... more Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale TFL is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spinorbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, TFL becomes arbitrarily small close to two new quantum critical points (QCPs) which we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω −1/5), orbital (ω 1/5) and spin-orbital (ω 1) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Physical Review B

Quantum impurity problems can be solved using the numerical renormalization group (NRG), which in... more Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a 'Wilson chain'. It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014)]. Here we systematically examine the accuracy and efficiency of the 'interleaved' NRG (iNRG) method in the context of the single impurity Anderson model, the twochannel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with 'standard' NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

Physical Review Letters

We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for... more We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transfered from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

AIP Conference Proceedings, 2006

ABSTRACT

Physical Review B, 2015

We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model ... more We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We find a ground state with trimerization (simplex) valence-bond order, and obtain the energy per site e 0 = −1.4099 (D = 16) by accurate calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of δ ≈ 20%. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state be a simplex valence-bond crystal (SVBC). We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground state phase diagram, find a quantum phase transition between the SVBC and a ferro-quadrupolar nematic state. Moreover, we implement non-abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

In addition to plateaus at integer values of G0= 2e^2/h, the linear conductance of a quantum poin... more In addition to plateaus at integer values of G0= 2e^2/h, the linear conductance of a quantum point contact shows an anomalous shoulder at around 0.7G0 -- the so-called 0.7-anomaly. Although the dependence of the 0.7-anomaly on parameters such as the temperature, the magnetic field, the bias voltage etc. has been widely studied, little is known about the influence of spin-orbit effects. We present a microscopic theory for the 0.7-anomaly, based on a one-dimensional tight binding model with a local on-site interaction, a smooth potential barrier and a homogeneous magnetic Zeeman field. In addition, we introduce Rashba and Dresselhaus terms into the Hamiltonian to capture the effect of spin-orbit coupling. We use a functional renormalization group approach to calculate the influence of interactions on the conductance at zero temperature. In this talk we present our theoretical predictions for the shape of the conductance curve, which depends strongly on the angle of the magnetic field ...

Physical Review B, 2001

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered.... more The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing d is larger than the bulk superconducting gap ⌬ and the small regime, where ⌬տd, is investigated analytically and numerically. The condensation energy, spin magnetization, and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by 1/ln N as a small parameter, where N is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant and is proportional to dN 2 ϭ 2 D. We find that also in a large regime with ⌬Ͼd, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly ⌬Ͼͱd D. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve and find a reentrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented, which suggest that in the large N limit the 1/N correction to the BCS result for the condensation energy is larger than ⌬.

Physical Review B, 2015

We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a clas... more We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially decaying correlations and can be interpreted as a (special) subset of the resonating Affleck-Kennedy-Lieb-Tasaki (AKLT) loop states. We provide a compact tensor network representation of the HSS states, with which we are able to calculate physical observables efficiently. We find that the HSS states have vanishing topological entanglement entropy, suggesting the absence of intrinsic topological order. We also employ the HSS states to perform a variational study of the spin-1 kagome Heisenberg antiferromagnetic model. When we use a restricted HSS ansatz preserving lattice symmetry, the best variational energy is found to be es = −1.3600; in contrast, another state with simplex valence-bond order (trimerization) and lower energy (es = −1.3871) is obtained when allowing lattice symmetry breaking.

ABSTRACT At sufficiently low temperatures, the dephasing time τ of mesoscopic samples is governed... more ABSTRACT At sufficiently low temperatures, the dephasing time τ of mesoscopic samples is governed by so-called Johnson-Nyquist (electronic) noise. We study the spatial dependence of the corresponding noise correlation function (NFC) in inhomogeneous systems. Using the fluctuation-dissipation theorem and the random-phase approximation, we derive a real-space integro-differential equation for the NCF and show that it reduces to a diffusion equation in the case of strong screening. In particular, using a method based on the spectral determinant, we evaluate the NCF for arbitrary networks of quasi-1D disordered wires with boundary conditions. As an application, we construct a realistic quantum dot model via a set of parallel wires connected at contacts to leads, and calculate the temperature dependence of τ as well as the quantum corrections to the conductance. Furthermore, we analyze the observability of the elusive 0D regime (reached at T < EThouless with the characteristic τT-2 behavior) in such systems, and discuss alternative scenarios of its observation.

Physical Review B, 2014

We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully ... more We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened N-channel Kondo model, namely cB, cT and cε, characterizing the magnetic field and temperature-dependence of the resisitivity, and the curvature of the equilibrium Kondo resonance, respectively. We present a compact, unified derivation of the N-dependence of these coefficients, combining elements from various previous treatments of this model. We numerically compute these coefficients using the numerical renormalization group, with non-Abelian symmetries implemented explicitly, finding agreement with Fermi-liquid predictions on the order of 5% or better.

Physical Review B, 2013

We investigate the effect of many-body interactions on the optical absorption spectrum of a charg... more We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intra dot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity model to include a static hole and a dynamic dot-electron scattering potential. The latter highlights the fact that an optically active dot acts as a tunable quantum impurity, enabling the investigation of a new dynamic regime of Fermi-edge physics.

Physical Review Letters, 2004

We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which c... more We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which can be described by a universal Hamiltonian. We show that an important class of spectral functions are dominated by one single state only, which implies the existence of well-defined (i.e. infinitelifetime) quasiparticles. Furthermore, the dominance of a single state enables us to calculate zerotemperature spectral functions with high accuracy using the density-matrix renormalization group. We illustrate the use of this method by calculating the tunneling density of states of metallic grains and the magnetic response of mesoscopic rings.

Physical Review Letters, 2001

We present detailed measurements of the discrete electron-tunneling level spectrum within nanomet... more We present detailed measurements of the discrete electron-tunneling level spectrum within nanometer-scale cobalt particles as a function of magnetic field and gate voltage, in this way probing individual quantum many-body eigenstates inside ferromagnetic samples. Variations among the observed levels indicate that different quantum states within one particle are subject to different magnetic anisotropy energies. Gate-voltage studies demonstrate that the low-energy tunneling spectrum is affected dramatically by the presence of non-equilibrium spin excitations.

We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ri... more We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we re-cently predicted a crossover for the dephasing time τϕ(T) from diffusive or ergodic 1D (τ−1ϕ ∝ T 2/3, T 1) to 0D behavior (τ−1ϕ ∝ T 2) as T drops below the Thouless energy ETh. 1 We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the 0D regime on equal foot-ing as the others. The crossover to 0D, predicted by Sivan, Imry and Aronov for 3D systems,2 has so far eluded experimental observation. We will show that for T ETh, 0D dephasing governs not only the T-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which re-sult only ...

Physical Review Letters

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, b... more Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale TFL is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spinorbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, TFL becomes arbitrarily small close to two new quantum critical points (QCPs) which we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω −1/5), orbital (ω 1/5) and spin-orbital (ω 1) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Physical Review B

Quantum impurity problems can be solved using the numerical renormalization group (NRG), which in... more Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a 'Wilson chain'. It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014)]. Here we systematically examine the accuracy and efficiency of the 'interleaved' NRG (iNRG) method in the context of the single impurity Anderson model, the twochannel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with 'standard' NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

Physical Review Letters

We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for... more We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transfered from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

AIP Conference Proceedings, 2006

ABSTRACT

Physical Review B, 2015

We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model ... more We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We find a ground state with trimerization (simplex) valence-bond order, and obtain the energy per site e 0 = −1.4099 (D = 16) by accurate calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of δ ≈ 20%. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state be a simplex valence-bond crystal (SVBC). We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground state phase diagram, find a quantum phase transition between the SVBC and a ferro-quadrupolar nematic state. Moreover, we implement non-abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

In addition to plateaus at integer values of G0= 2e^2/h, the linear conductance of a quantum poin... more In addition to plateaus at integer values of G0= 2e^2/h, the linear conductance of a quantum point contact shows an anomalous shoulder at around 0.7G0 -- the so-called 0.7-anomaly. Although the dependence of the 0.7-anomaly on parameters such as the temperature, the magnetic field, the bias voltage etc. has been widely studied, little is known about the influence of spin-orbit effects. We present a microscopic theory for the 0.7-anomaly, based on a one-dimensional tight binding model with a local on-site interaction, a smooth potential barrier and a homogeneous magnetic Zeeman field. In addition, we introduce Rashba and Dresselhaus terms into the Hamiltonian to capture the effect of spin-orbit coupling. We use a functional renormalization group approach to calculate the influence of interactions on the conductance at zero temperature. In this talk we present our theoretical predictions for the shape of the conductance curve, which depends strongly on the angle of the magnetic field ...

Physical Review B, 2001

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered.... more The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing d is larger than the bulk superconducting gap ⌬ and the small regime, where ⌬տd, is investigated analytically and numerically. The condensation energy, spin magnetization, and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by 1/ln N as a small parameter, where N is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant and is proportional to dN 2 ϭ 2 D. We find that also in a large regime with ⌬Ͼd, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly ⌬Ͼͱd D. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve and find a reentrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented, which suggest that in the large N limit the 1/N correction to the BCS result for the condensation energy is larger than ⌬.

Physical Review B, 2015

We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a clas... more We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially decaying correlations and can be interpreted as a (special) subset of the resonating Affleck-Kennedy-Lieb-Tasaki (AKLT) loop states. We provide a compact tensor network representation of the HSS states, with which we are able to calculate physical observables efficiently. We find that the HSS states have vanishing topological entanglement entropy, suggesting the absence of intrinsic topological order. We also employ the HSS states to perform a variational study of the spin-1 kagome Heisenberg antiferromagnetic model. When we use a restricted HSS ansatz preserving lattice symmetry, the best variational energy is found to be es = −1.3600; in contrast, another state with simplex valence-bond order (trimerization) and lower energy (es = −1.3871) is obtained when allowing lattice symmetry breaking.

ABSTRACT At sufficiently low temperatures, the dephasing time τ of mesoscopic samples is governed... more ABSTRACT At sufficiently low temperatures, the dephasing time τ of mesoscopic samples is governed by so-called Johnson-Nyquist (electronic) noise. We study the spatial dependence of the corresponding noise correlation function (NFC) in inhomogeneous systems. Using the fluctuation-dissipation theorem and the random-phase approximation, we derive a real-space integro-differential equation for the NCF and show that it reduces to a diffusion equation in the case of strong screening. In particular, using a method based on the spectral determinant, we evaluate the NCF for arbitrary networks of quasi-1D disordered wires with boundary conditions. As an application, we construct a realistic quantum dot model via a set of parallel wires connected at contacts to leads, and calculate the temperature dependence of τ as well as the quantum corrections to the conductance. Furthermore, we analyze the observability of the elusive 0D regime (reached at T < EThouless with the characteristic τT-2 behavior) in such systems, and discuss alternative scenarios of its observation.

Physical Review B, 2014

We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully ... more We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened N-channel Kondo model, namely cB, cT and cε, characterizing the magnetic field and temperature-dependence of the resisitivity, and the curvature of the equilibrium Kondo resonance, respectively. We present a compact, unified derivation of the N-dependence of these coefficients, combining elements from various previous treatments of this model. We numerically compute these coefficients using the numerical renormalization group, with non-Abelian symmetries implemented explicitly, finding agreement with Fermi-liquid predictions on the order of 5% or better.

Physical Review B, 2013

We investigate the effect of many-body interactions on the optical absorption spectrum of a charg... more We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intra dot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity model to include a static hole and a dynamic dot-electron scattering potential. The latter highlights the fact that an optically active dot acts as a tunable quantum impurity, enabling the investigation of a new dynamic regime of Fermi-edge physics.

Physical Review Letters, 2004

We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which c... more We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which can be described by a universal Hamiltonian. We show that an important class of spectral functions are dominated by one single state only, which implies the existence of well-defined (i.e. infinitelifetime) quasiparticles. Furthermore, the dominance of a single state enables us to calculate zerotemperature spectral functions with high accuracy using the density-matrix renormalization group. We illustrate the use of this method by calculating the tunneling density of states of metallic grains and the magnetic response of mesoscopic rings.

Physical Review Letters, 2001

We present detailed measurements of the discrete electron-tunneling level spectrum within nanomet... more We present detailed measurements of the discrete electron-tunneling level spectrum within nanometer-scale cobalt particles as a function of magnetic field and gate voltage, in this way probing individual quantum many-body eigenstates inside ferromagnetic samples. Variations among the observed levels indicate that different quantum states within one particle are subject to different magnetic anisotropy energies. Gate-voltage studies demonstrate that the low-energy tunneling spectrum is affected dramatically by the presence of non-equilibrium spin excitations.