arXiv subjects

Jan von Delft

Publications and source records attributed to Jan von Delft.

At least 91 records · Page 5Linked to original sources

arXiv2017

Keldysh Derivation of Oguri's Linear Conductance Formula for Interacting Fermions

We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalisum, for the linear conductance through a central, interacting region coupled to non-interacting fermionic leads. Our starting point is the well-known Meir-Wingreen formula for the current, whose derivative w.r.t.\ to the source-drain voltage yields the conductance. We perform this derivative analytically, by exploiting an exact flow equation from the functional renormalization group, which expresses the flow w.r.t.\ voltage of the self-energy in terms of the two-particle vertex. This yields a Keldysh-based formulation of Oguri's formula for the linear conductance, which facilitates applying it in the context of approximation schemes formulated in the Keldysh formalism. (Generalizing our approach to the non-linear conductance is straightforward, but not pursued here.) -- We illustrate our linear conductance formula within the context of a model that has previously been shown to capture the essential physics of a quantum point contact in the regime of the 0.7 anomaly. The model involves a tight-binding chain with a one-dimensional potential barrier and onsite interactions, which we treat using second order perturbation theory. We show that numerical costs can be reduced significantly by using a non-uniform lattice spacing, chosen such that the occurence of artificial bound states close to the upper band edge is avoided.

cond-mat.str-el↗

arXiv2017

Open Wilson chains for quantum impurity models: Keeping track of all bath modes

When constructing a Wilson chain to represent a quantum impurity model, the effects of truncated bath modes are neglected. We show that their influence can be kept track of systematically by constructing an "open Wilson chain" in which each site is coupled to a separate effective bath of its own. As a first application, we use the method to cure the so-called mass-flow problem that can arise when using standard Wilson chains to treat impurity models with asymmetric bath spectral functions at finite temperature. We demonstrate this for the strongly sub-Ohmic spin-boson model at quantum criticality where we directly observe the flow towards a Gaussian critical fixed point.

cond-mat.str-el↗

arXiv2017

Spin fluctuations in the 0.7-anomaly in quantum point contacts

It has been argued that the 0.7 anomaly in quantum point contacts (QPCs) is due to an enhanced density of states at the top of the QPC-barrier (van Hove ridge), which strongly enhances the effects of interactions. Here, we analyze their effect on dynamical quantities. We find that they pin the van Hove ridge to the chemical potential when the QPC is subopen; cause a temperature dependence for the linear conductance that qualitatively agrees with experiment; strongly enhance the magnitude of the dynamical spin susceptibility; and significantly lengthen the QPC traversal time. We conclude that electrons traverse the QPC via a slowly fluctuating spin structure of finite spatial extent.

cond-mat.mes-hall↗

arXiv2017

Anatomy of quantum critical wave functions in dissipative impurity problems

Quantum phase transitions reflect singular changes taking place in a many-body ground state, however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. New physical insights into the sub-Ohmic spin-boson model are provided by the coherent state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking, while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix product states (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.

cond-mat.str-el↗

arXiv2017

Functional Renormalization Group Approach for Inhomogeneous One-Dimensional Fermi Systems with Finite-Ranged Interactions

We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third order truncated form of fRG, the dependence of the two-particle vertex is described by O(N^4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Phys. Rev. B 89, 045128 (2014)], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O(N^2) independent variables. Here, we extend this scheme to the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L, using O(N^2 L^2) independent variables for the vertex. We apply the eCLA to three types of one-dimensional models : First, to a quantum point contact (QPC) with a parabolic barrier top and short-ranged interactions. Here eCLA achieves convergence for L equal to the characteristic length l_x of the QPC. It also turns out that the additional feedback stabilizes the fRG-flow. This enables us, second, to study the crossover between a QPC and a quantum dot, again for a model with short-ranged interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Estimating the form of such a finite-ranged interaction in a QPC, we study its effects on the conductance and the density. For low densities and sufficiently large interaction ranges the conductance develops additional oscillatory features, and the corresponding density shows fluctuations that can be interpreted as Friedel oscillations arising from a renormalized barrier shape with a rather flat top and steep flanks.

cond-mat.str-el↗

arXiv2016

Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit

The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.

cond-mat.str-el↗

arXiv2016

Dynamic structure factor of the spin-1/2 XXZ chain in a transverse field

The spin-$\frac{1}{2}$ XXZ chain with easy-plane anisotropy in a transverse field describes well the thermodynamic properties of the material ${\rm Cs_2CoCl_4}$ in a wide range of temperatures and fields including the region close to the spin-flop Ising quantum phase transition. For a comparison with prospective inelastic neutron scattering experiments on this compound, we present results of an extensive numerical study of its dynamic structure factor $\mathcal{S}^{αβ}(k,ω)$ using matrix-product-state (MPS) techniques. Close to criticality, the dynamic part of the correlator $\mathcal{S}^{xx}$ longitudinal to the applied field is incoherent and possesses a small total weight as the ground state is already close to saturation. The transverse correlator $\mathcal{S}^{zz}$, on the other hand, is dominated by a coherent single-particle excitation with additional spectral weight at higher energies that we tentatively attribute to a repulsively bound pair of particles. With increasing temperature, the latter quickly fades and spectral weight instead accumulates close to zero wavevector just above the single-particle energy. On a technical level, we compare the numerical efficiency of real-time evolution to an MPS-based Chebyshev expansion in the present context, finding that both methods yield results of similar quality at comparable numerical costs.

cond-mat.str-el↗

arXiv2015

Symmetric Minimally Entangled Typical Thermal States

We extend White's minimally entangled typically thermal states approach (METTS) to allow Abelian and non-Ablian symmetries to be exploited when computing finite-temperature response functions in one-dimensional (1D) quantum systems. Our approach, called SYMETTS, starts from a METTS sample of states that are not symmetry eigenstates, and generates from each a symmetry eigenstate. These symmetry states are then used to calculate dynamic response functions. SYMETTS is ideally suited to determine the low-temperature spectra of 1D quantum systems with high resolution. We employ this method to study a generalized diamond chain model for the natural mineral azurite Cu${}_3$(CO${}_3)_2$(OH$)_2$, which features a plateau at $\frac{1}{3}$ in the magnetization curve at low temperatures. Our calculations provide new insight into the effects of temperature on magnetization and excitation spectra in the plateau phase, which can be fully understood in terms of the microscopic model.

cond-mat.str-el↗

arXiv2015

Fermi-liquid theory for the single-impurity Anderson model

We generalize Nozières' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozières that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the $\sim B^2$, $\sim T^2$, and $\sim V^2$ terms \textit{exactly} in terms of the Fermi-liquid parameters. The coefficients of $T^2$, $V^2$ and $B^2$ are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

cond-mat.mes-hall↗

arXiv2015

Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet

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 per site is found to be $e_0 = -1.3600$. In contrast, when allowing lattice symmetry breaking, we find a trimerized simplex valence bond crystal with a lower energy, $e_0=-1.3871$.

cond-mat.str-el↗

arXiv2015

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site {$e_0=-1.41090(2)$ with $D^*=8$ multiplets retained (i.e., a bond dimension of $D=24$), and $e_0=-1.4116(4)$ from large-$D$ extrapolation,} by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $δ\approx$ 19\%, i.e, there is a trimerization (simplex) valence-bond order in the ground state. 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. 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.

cond-mat.str-el↗

arXiv2015

Effect of spin-orbit interactions on the 0.7 anomaly in quantum point contacts

We study how the conductance of a quantum point contact is affected by spin-orbit interactions, for systems at zero temperature both with and without electron-electron interactions. In the presence of spin-orbit coupling, tuning the strength and direction of an external magnetic field can change the dispersion relation and hence the local density of states in the point contact region. This modifies the effect of electron-electron interactions, implying striking changes in the shape of the 0.7-anomaly and introducing additional distinctive features in the first conductance step.

cond-mat.mes-hall↗

arXiv2014

Two-bath spin-boson model: Phase diagram and critical properties

The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum phase transition. Here we present a detailed study of a U(1)-symmetric two-bath spin-boson model, where two different components of an SU(2) spin 1/2 are coupled to separate dissipative baths. Non-trivial physics arises from the competition of the two dissipation channels, resulting in a variety of phases and quantum phase transitions. We employ a combination of analytical and numerical techniques to determine the properties of both the stable phases and the quantum critical points. In particular, we find a critical intermediate-coupling phase which is bounded by a continuous quantum phase transition which violates the quantum-to-classical correspondence.

cond-mat.stat-mech↗

arXiv2014

On the relation between the 0.7-anomaly and the Kondo effect: Geometric Crossover between a Quantum Point Contact and a Kondo Quantum Dot

Quantum point contacts (QPCs) and quantum dots (QDs), two elementary building blocks of semiconducting nanodevices, both exhibit famously anomalous conductance features: the 0.7-anomaly in the former case, the Kondo effect in the latter. For both the 0.7-anomaly and the Kondo effect, the conductance shows a remarkably similar low-energy dependence on temperature $T$, source-drain voltage $V_{\rm sd}$ and magnetic field $B$. In a recent publication [F. Bauer et al., Nature, 501, 73 (2013)], we argued that the reason for these similarities is that both a QPC and a KQD feature spin fluctuations that are induced by the sample geometry, confined in a small spatial regime, and enhanced by interactions. Here we further explore this notion experimentally and theoretically by studying the geometric crossover between a QD and a QPC, focussing on the $B$-field dependence of the conductance. We introduce a one-dimensional model that reproduces the essential features of the experiments, including a smooth transition between a Kondo QD and a QPC with 0.7-anomaly. We find that in both cases the anomalously strong negative magnetoconductance goes hand in hand with strongly enhanced local spin fluctuations. Our experimental observations include, in addition to the Kondo effect in a QD and the 0.7-anomaly in a QPC, Fano interference effects in a regime of coexistence between QD and QPC physics, and Fabry-Perot-type resonances on the conductance plateaus of a clean QPC. We argue that Fabry-Perot-type resonances occur generically if the electrostatic potential of the QPC generates a flatter-than-parabolic barrier top.

cond-mat.str-el↗

arXiv2014

Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo model

We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened $N$-channel Kondo model, namely $c_B$, $c_T$ and $c_\varepsilon$, 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.

cond-mat.str-el↗

arXiv2014

Functional Renormalization Group Approach for Inhomogeneous Interacting Fermi-Systems

The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g. sites of a real-space discretization). In order to include the flow equation for the two-particle vertex one needs to make further approximations if $N$ becomes too large. We present such an approximation scheme, called the coupled-ladder approximation, for the special case of onsite interaction. Like the generic third-order-truncated fRG, the coupled-ladder approximation is exact to second order and is closely related to a simultaneous treatment of the random phase approximation in all channels, i.e. summing up parquet-type diagrams. The scheme is applied to a one-dimensional model describing a quantum point contact.

cond-mat.str-el↗

arXiv2014

Identifying Symmetry-Protected Topological Order by Entanglement Entropy

According to the classification using projective representations of the SO(3) group, there exist two topologically distinct gapped phases in spin-1 chains. The symmetry-protected topological (SPT) phase possesses half-integer projective representations of the SO(3) group, while the trivial phase possesses integer linear representations. In the present work, we implement non-Abelian symmetries in the density matrix renormalization group (DMRG) method, allowing us to keep track of (and also control) the virtual bond representations, and to readily distinguish the SPT phase from the trivial one by evaluating the multiplet entanglement spectrum. In particular, using the entropies $S^I$ ($S^H$) of integer (half-integer) representations, we can define an entanglement gap $G = S^I - S^H$, which equals 1 in the SPT phase, and $-1$ in the trivial phase. As application of our proposal, we study the spin-1 models on various 1D and quasi-1D lattices, including the bilinear-biquadratic model on the single chain, and the Heisenberg model on a two-leg ladder and a three-leg tube. Among others, we confirm the existence of an SPT phase in the spin-1 tube model, and reveal that the phase transition between the SPT and the trivial phase is a continuous one. The transition point is found to be critical, with conformal central charge $c=3$ determined by fits to the block entanglement entropy.

cond-mat.str-el↗

arXiv2013

The quantum transverse-field Ising chain in circuit QED: effects of disorder on the nonequilibrium dynamics

We study several dynamical properties of a recently proposed implementation of the quantum transverse-field Ising chain in the framework of circuit QED. Particular emphasis is placed on the effects of disorder on the nonequilibrium behavior of the system. We show that small amounts of fabrication-induced disorder in the system parameters do not jeopardize the observation of previously-predicted phenomena. Based on a numerical extraction of the mean free path of the system, we also provide a simple quantitative estimate for certain disorder effects on the nonequilibrium dynamics of the circuit QED quantum simulator. We discuss the transition from weak to strong disorder, characterized by the onset of Anderson localization of the system's wave functions, and the qualitatively different dynamics it leads to.

cond-mat.mes-hall↗