Renormalization Group Calculations Research Articles

Enhanced nematicity emerging from higher-order Van Hove singularities

Motivated by the experimental identification of a higher-order Van Hove singularity (VHS) in $A{\text{V}}_{3}{\mathrm{Sb}}_{5}$ kagome metals, we study electronic instabilities of two-dimensional lattice models with higher-order VHS and flavor degeneracy. In contrast to conventional VHSs, the larger power-law density of states and the weaker nesting propensity of higher-order VHSs conspire together to generate distinct competing instabilities. After discussing the occurrence of higher-order VHSs on square and kagome lattice models, we perform unbiased renormalization group calculations to study competing instabilities and find a rich phase diagram containing ferromagnetism, antiferromagnetism, superconductivity, and Pomeranchuk orders. Remarkably, there is a generic transition from superconductivity to a $d$-wave Pomeranchuk order with increasing flavor number. Implications for the intriguing quantum states of $A{\text{V}}_{3}{\mathrm{Sb}}_{5}$ kagome metals are also discussed.

Z_{3} Parafermion in the Double Charge Kondo Model.

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [W. Pouse et al., Nat. Phys. (2023)NPAHAX1745-247310.1038/s41567-022-01905-4] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here, we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z_{3} parafermion emerges at the critical point, characterized by a fractional 1/2ln(3) residual entropy, and scattering fractional charges e/3. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

Comparative study of charge order in undoped infinite-layer nickelate superconductors

To understand the microscopic mechanism of the charge order observed in the parent compound of the infinite-layer nickelate superconductors, we consider a minimal three-legged model consisting of a two-legged Hubbard ladder for the Ni $3d_{x^2-y^2}$ electrons and a free conduction electron chain from the rare-earths. With highly accurate density matrix renormalization group calculations, when the chemical potential difference is adjusted to make the Hubbard ladder with $1/3$ hole doping, we find a long-range charge order with period $3$ in the ground state of the model, while the spin excitation has a small energy gap. Moreover, the electron pair-pair correlation has a quasi-long-range behavior, indicating an instability of superconductivity even at half-filling. As a comparison, the same method is applied to a pure two-legged Hubbard model with $1/3$ hole doping in which the period-3 charge order is a quasi-long range one. The difference between them demonstrates that the free electron chain of the three-legged ladder plays the role of a charge reservoir and enhances the charge order in the undoped infinite-layer nickelates.

Quantum spin liquid in an RKKY-coupled two-impurity Kondo system

We consider a 2-impurity Kondo system with spin-exchange coupling within the conduction band. Our numerical renormalization group calculations show that for strong intraband spin correlations the competition of these correlations with Kondo spin screening stabilizes a metallic spin-liquid phase of the localized spins without geometric frustration. For weak Kondo coupling the spin liquid and the Kondo singlet phase are separated by two quantum phase transitions and an intermediate RKKY spin-dimer phase, while beyond a critical coupling they are connected by a crossover. The results suggest how a quantum spin liquid may be realized in heavy-fermion systems near a spin-density wave instability.

Majorana Coupling and Kondo Screening of Localized Spins

We perform a theoretical analysis of the fate of local magnetic moment of a quantum dot coupled to a normal metallic lead and a topological superconducting wire hosting Majorana modes at the ends. By means of simple analytical tools and numerical renormalization group calculations we show that the proximity of Majorana mode reduces the magnetic moment from $1/4$, characteristic of a free spin $1/2$, to $1/16$. The coupling to the normal lead then causes the Kondo effect, such that the magnetic moment is fully screened below the Kondo temperature. The latter is vastly increased for strong coupling to Majorana mode.

Superconductivity of repulsive spinless fermions with sublattice potentials

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered $d$-wave and $f$-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the square lattice displays a much richer phase diagram including topological $p+ip$ superconductivity which is induced by a qualitatively different mechanism compared to the $d$-wave pairing. We illuminate this from several complementary perspectives: We analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive functional renormalization group and and density matrix renormalization group calculations.

Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model

We study the effects of thermal fluctuations and pinned boundaries in graphene membranes by using a phase-field crystal model with out-of-plane deformations. For sufficiently long times, the linear diffusive behavior of height fluctuations in systems with free boundaries becomes a saturation regime, while at intermediate times the behavior is still subdiffusive as observed experimentally. Under compression, we find mirror buckling fluctuations where the average height changes from above to below the pinned boundaries, with the average time between fluctuations diverging below a critical temperature corresponding to a thermally induced buckling transition. Near the transition, we find a nonlinear height response in agreement with recent renormalization-group calculations and observed in experiments on graphene membranes under an external transverse force with clamped boundaries.

Pair density wave and loop current promoted by Van Hove singularities in moiré systems

We theoretically show that in the presence of conventional or higher order Van Hove singularities (VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux $3\ensuremath{\phi}$ in each triangular plaquette at $\ensuremath{\phi}=\ensuremath{\pi}/3$ and $\ensuremath{\pi}/6$ in moir\'e systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state under certain conditions through the renormalization group calculation and a flux insertion argument. Moreover, we also find that a topological nontrivial loop current order becomes the leading instability if the Fermi surface with conventional VHS is perfectly nested at $\ensuremath{\phi}=\ensuremath{\pi}/3$. Similar to the Haldane model, this loop current state has the quantum anomalous Hall effect. If we dope this loop current state or introduce a finite next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$, the chiral $d$-wave PDW becomes the dominant instability. Experimentally, the flux can be effectively tuned by an out-of-plane electric field in moir\'e systems based on graphene and transition metal dichalcogenides.

Mutual information prediction for strongly correlated systems

We have trained a new machine-learning (ML) model which predicts mutual information (MI) for strongly correlated systems. This is a complex quantity, which is much more difficult to predict than one-site entropies, but carries important information about the correlation structure inside electronic systems. In this work, we replaced the expensive density matrix renormalization group (DMRG) calculations by newly trained ML model for prediction of the mutual information. We show the performance of the model on two important tasks: (a) to determine the correlation structure and (b) to determine ordering of orbitals for accurate DMRG calculations. The results are compared with the MI obtained from accurate DMRG calculations.

Unraveling the nature of spin excitations disentangled from charge contributions in a doped cuprate superconductor

The nature of the spin excitations in superconducting cuprates is a key question toward a unified understanding of the cuprate physics from long-range antiferromagnetism to superconductivity. The intense spin excitations up to the over-doped regime revealed by resonant inelastic X-ray scattering bring new insights as well as questions like how to understand their persistence or their relation to the collective excitations in ordered magnets (magnons). Here, we study the evolution of the spin excitations upon hole-doping the superconducting cuprate Bi2Sr2CaCu2O8+δ by disentangling the spin from the charge excitations in the experimental cross section. We compare our experimental results against density matrix renormalization group calculations for a t-J-like model on a square lattice. Our results unambiguously confirm the persistence of the spin excitations, which are closely connected to the persistence of short-range magnetic correlations up to high doping. This suggests that the spin excitations in hole-doped cuprates are related to magnons—albeit short-ranged.

Kardar-Parisi-Zhang universality class in (d+1)-dimensions.

The determination of the exact exponents of the KPZ class in any substrate dimension d is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences for other growth equations, I find here that the KPZ growth exponents (related to the temporal scaling of the fluctuations) are given by β_{d}=7/8d+13. These exponents present an excellent agreement with the most accurate estimates for them in the literature. Moreover, they are confirmed here through extensive Monte Carlo simulations of discrete growth models and real-space renormalization group (RG) calculations for directed polymers in random media (DPRM), up to d=15. The left-tail exponents of the probability density functions for the DPRM energy provide another striking verification of the analytical result above.

Entropy Measurement of a Strongly Coupled Quantum Dot.

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

Gradient corrections to the local-density approximation in the one-dimensional Bose gas

The local density approximation (LDA) is the central technical tool in the modeling of quantum gases in trapping potentials. It consists in treating the gas as an assembly of independent mesoscopic fluid cells at equilibrium with a local chemical potential, and it is justified when the correlation length is larger than the size of the cells. The LDA is often regarded as a crude approximation, particularly in the ground state of the one-dimensional (1D) Bose gas, { where the correlation length is "therefore said to be" infinite (in the sense that correlation functions decay as a power law).} Here we take another look at the LDA. The local density $\rho(x)$ is viewed as a functional of the trapping potential $V(x)$, to which one applies a gradient expansion. The zeroth order in that expansion is the LDA. The first-order correction in the gradient expansion vanishes due to reflection symmetry. At second order, there are two corrections proportional to $d^2V/dx^2$ and $(dV/dx)^2$, and we propose a method to determine the corresponding coefficients by a perturbative calculation in the Lieb-Liniger model. This leads to an expression for the coefficients in terms of matrix elements of the density operator, which can in principle be evaluated numerically for an arbitrary coupling constant; here we show how to efficiently evaluate the coefficient associated to the curvature of the potential $d^2V/dx^2$, which dominates the deviation to LDA near local minima or maxima of the trapping potential. Both coefficients are evaluated analytically in the limits of infinite repulsion (hard-core bosons) and small repulsion (quasi-condensate).} The corrected LDA density profiles are compared to DMRG calculations, with significant improvement compared to zeroth-order LDA.

Emergent many-body composite excitations of interacting spin-1/2 trimers

Understanding exotic forms of magnetism in quantum spin systems is an emergent topic of modern condensed matter physics. Quantum dynamics can be described by particle-like carriers of information, known-as quasiparticles that appear from the collective behaviour of the underlying system. Spinon excitations, governing the excitations of quantum spin-systems, have been accurately calculated and precisely verified experimentally for the antiferromagnetic chain model. However, identification and characterization of novel quasiparticles emerging from the topological excitations of the spin system having periodic exchange interactions are yet to be obtained. Here, we report the identification of emergent composite excitations of the novel quasiparticles doublons and quartons in spin-1/2 trimer-chain antiferromagnet Na2Cu3Ge4O12 (having periodic intrachain exchange interactions J1-J1-J2) and its topologically protected quantum 1/3 magnetization-plateau state. The characteristic energies, dispersion relations, and dynamical structure factor of neutron scattering as well as macroscopic quantum 1/3 magnetization-plateau state are in good agreement with the state-of-the-art dynamical density matrix renormalization group calculations.

Tensor network approach to 2D Lorentzian quantum Regge calculus

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries, although the investigation of the higher moments is required to make the statement more conclusive. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

Fermionic interpretation of the quantum phase transition in XXZ magnets

Quantum phase transitions in quantum magnets constitute an important field that has attracted great interests. Although a variety of analytic and numerical methods have been introduced in this direction, faithful fermionic descriptions are still desired because they can transform the spin models to a form tractable by conventional many-body techniques, yielding more transparent physical pictures. We generalize the Chern-Simons fermionization approach and apply it to the XXZ quantum magnets. After fermionzation, the Ising interaction of the XXZ spin model leads to a fermion-fermion interaction. We show that the additional fermion-fermion interaction generates an interesting phase transition between two fermionic ordered states, i.e., the Chern-Simons superconductor and the Chern-Simons exciton insulator. We also demonstrate that this transition in the fermionic language essentially describes the quantum phase transition between the planar and out-of-plane N\'eel orders in the spin picture. The fermionic mean-field theory further leads to a nonlinear $\ensuremath{\sigma}$ model that describes the quantum phase transition, which is further supported by our density matrix renormalization group calculations in the original spin model. Our work introduces a fermionic interpretation of quantum phase transitions and advances the existing knowledge of quantum magnets.

One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time dependent density matrix renormalization group calculations, we numerically compute the one body reduced density matrix for the J-V model, as well as its post-quench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

Hallmarks of Majorana mode leaking into a hybrid double quantum dot

We investigate the spectral and transport properties of a double quantum dot laterally attached to a topological superconducting nanowire, hosting the Majorana zero-energy modes. Specifically, we consider a geometry, in which the outer quantum dot is embedded between the external normal and superconducting leads, forming a circuit. First, we derive analytical expressions for the bound states in the case of an uncorrelated system and discuss their signatures in the tunneling spectroscopy. Then, we explore the case of strongly correlated quantum dots by performing the numerical renormalization group calculations, focusing on the interplay and relationship between the leaking Majorana mode and the Kondo states on both quantum dots. Finally, we discuss feasible means to experimentally probe the in-gap quasiparticles by using the Andreev spectroscopy based on the particle-to-hole scattering mechanism.

Excitation spectra of fully correlated donor-acceptor complexes by density matrix renormalisation group

In this paper, we investigate the convergence properties of density matrix renormalisation group (DMRG) calculations for vertical electronic excitations performed on three bimolecular complexes motivated by Szalay's recent benchmark results [JCTC. 2020;16:7]. Besides the high-level coupled-cluster reference spectrum, the extrapolated truncation-free DMRG results are compared against several alternative solutions based on multireference configuration interaction and coupled-cluster theories. By taking advantage of the error cancellation effects, which are inherent in the state-averaged computational scheme, we demonstrate that the extrapolated solution based on only low bond-dimensional DMRG data could already provide quantitative predictions even for large active spaces. We also show that orbital optimisation improves further the accuracy of the DMRG results which systematically approach the excitation energies of coupled cluster single-double-triple at similar computational costs.

Designer flat bands: Topology and enhancement of superconductivity

We construct quasi one-dimensional topological and non-topological three-band lattices with tunable band gap and winding number of the flat band. Using mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We show excellent agreement between MF and DMRG. When a phase twist is applied on the system, a phase difference appears between pairing order parameters on different sublattices, and this plays a very important role in the SC density. The SC weight, $D_s$, on the gapped topological, $W\neq0$, flat band increases linearly with interaction strength, $U$, for low values, and with a slope that depends on the details of the compact localized state at $U=0$. As $U\to 0$ for the gapped non-topological flat band ($W=0$), $D_s$ decays with a power law faster than quadratic but slower than exponential. This indicates that isolated non-topological flat bands are less beneficial to SC. In the gapless case (flat band touching the band above it), we find at low $U$ (both for $W=0$ and $W\neq 0$) that $D_s\propto U^\varphi$ with $\varphi<1$ contrary to the $U{\rm ln}\, ({\rm const.}/U)$ behavior reported in the literature. In other words, $D_s$ increases faster than linearly for low $U$ thus favoring SC at weak interaction more than the gapped case. For systems with touching bands, we observe that the one-body correlation length, $\xi$, diverges as a power law as $U\rightarrow0$, while for the isolated flat band $\xi(U\to 0)$ is a constant smaller than one lattice spacing. Both behaviors are distinct from the exponential divergence of $\xi$ in the dispersive case. Our results re-establish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.