Exact Renormalization Group Method Research Articles

Minimizing non-radiative decay in molecular aggregates through control of excitonic coupling

The widely known “Energy Gap Law” (EGL) predicts a monotonically exponential increase in the non-radiative decay rate (knr) as the energy gap narrows, which hinders the development of near-infrared (NIR) emissive molecular materials. Recently, several experiments proposed that the exciton delocalization in molecular aggregates could counteract EGL to facilitate NIR emission. In this work, the nearly exact time-dependent density matrix renormalization group (TD-DMRG) method is developed to evaluate the non-radiative decay rate for exciton-phonon coupled molecular aggregates. Systematical numerical simulations show, by increasing the excitonic coupling, knr will first decrease, then reach a minimum, and finally start to increase to follow EGL, which is an overall result of two opposite effects of a smaller energy gap and a smaller effective electron-phonon coupling. This anomalous non-monotonic behavior is found robust in a number of models, including dimer, one-dimensional chain, and two-dimensional square lattice. The optimal excitonic coupling strength that gives the minimum knr is about half of the monomer reorganization energy and is also influenced by system size, dimensionality, and temperature.

Dimensional crossover on multileg attractive- U Hubbard ladders

We study the ground state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density matrix renormalization group method simulations, we construct grand canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

Tunable stripe order and weak superconductivity in the Moiré Hubbard model

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we study the superconducting correlation function and point out the possibility of weak superconductivity.

Multipartite entanglement in the random Ising chain

Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ensuremath{\ell}$ separated by a distance $r=\ensuremath{\alpha}\ensuremath{\ell}$ and quantify their entanglement negativity ($\mathcal{E}$) and mutual information ($\mathcal{I}$) in critical random Ising chains. We find universal constant $\mathcal{E}(\ensuremath{\alpha})$ and $\mathcal{I}(\ensuremath{\alpha})$ over any distances, using the asymptotically exact strong disorder renormalization group method. Our results are qualitatively different from both those in the clean Ising model and random spin chains of a singlet ground state, like the spin-$\frac{1}{2}$ random Heisenberg chain and the random XX chain. While for random singlet states $\mathcal{I}(\ensuremath{\alpha})/\mathcal{E}(\ensuremath{\alpha})=2$, in the random Ising chain this universal ratio is strongly $\ensuremath{\alpha}$ dependent. This deviation between systems contrasts with the behavior of the entanglement entropy of a single subsystem, for which the various random critical chains and clean models give the same qualitative behavior. The reason is that $\mathcal{E}$ and $\mathcal{I}$ are sensitive to higher order correlations in the ground-state structure. Therefore, studying multipartite entanglement provides additional universal information in random quantum systems, beyond what we can learn from a single subsystem.

Transient dynamics of a magnetic impurity coupled to superconducting electrodes: Exact numerics versus perturbation theory

Impurities coupled to superconductors offer a controlled platform to understand the interplay between superconductivity, many-body interactions, and nonequilibrium physics. In the equilibrium situation, local interactions at the impurity induce a transition from the spin-singlet to the spin-doublet ground state, resulting in a supercurrent sign reversal ($0\text{\ensuremath{-}}\ensuremath{\pi}$ transition). In this work, we apply the exact time-dependent density matrix renormalization group method to simulate the transient dynamics of such superconducting systems. We also use a perturbative approximation to analyze their properties at longer times. These two methods agree for a wide range of parameters. In a phase-biased situation, the system gets trapped in a metastable state characterized by a lower supercurrent compared to the equilibrium case. We show that local Coulomb interactions do not provide an effective relaxation mechanism for the initially trapped quasiparticles. In contrast, other relaxation mechanisms, such as coupling to a third normal lead, make the impurity spin relax for parameter values corresponding to the equilibrium 0 phase. For parameters corresponding to the equilibrium $\ensuremath{\pi}$ phase the impurity converges to a spin-polarized stationary state. Similar qualitative behavior is found for a voltage-biased junction, which provides an effective relaxation mechanism for the trapped quasiparticles in the junction.

Time-dependent density matrix renormalization group coupled with n-mode representation potentials for the excited state radiationless decay rate: Formalism and application to azulene

We propose a method for calculating the non-radiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C–H vibrations to receive electronic energy while C–H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

Phase transitions of bosonic fractional quantum Hall effect in topological flat bands

We study the phase transitions of bosonic $\ensuremath{\nu}=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.

Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields

Motivated by the magnetic phase transition of a proximate Kitaev system $\alpha$-RuCl$_3$ in the presence of a magnetic field, we study the simplest but essential quantum spin model with the ferromagnetic nearest neighboring (NN) Kitaev interaction and additional antiferromagnetic third NN Heisenberg interaction. Employing both exact diagonalization and density matrix renormalization group methods, we demonstrate that the model shows the magnetic phase transition from the zigzag order phase to the spin polarized phase through an intermediate phase in both cases when an in-plane magnetic field is applied perpendicular to the NN bond direction and when an out-of-plane field is applied, in good agreement with experimental observations. Furthermore, we verify that additional symmetric off-diagonal $\Gamma$ interaction and ferromagnetic Heisenberg interaction between NN spins can both suppress the intermediate phase with the in-plane field. Our result gives important clues on determining relevant interactions in the field-induced magnetic phase transition of proximate Kiteav systems.

Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.

Topological end states in a one-dimensional spatially modulated interaction spinless fermion model

The effect of spatially modulated interaction on quantum phase transition in one-dimensional interacting spinless fermion system is theoretically investigated by exact diagonalization and density matrix renormalization group method. Our calculations show that the periodically modulated interaction can drive the spinless fermion system into topological charge density wave state. The topological state is encoded by quasiparticle end states and the fractional quantized e/2 end charges, and characterized by Berry phase and Chern number. The quasiparticle energy spectra as a function of modulated interaction period appears a stunning fractal-like structure. For the quasi-periodic case, the topological phase transition can also occur. In a word, the spatially modulated interaction can be a new elegant avenue towards realizing to interacting topological phases.

Two-magnon bound states in the Kitaev model in a [111] field

It is now well established that the Kitaev honeycomb model in a magnetic field along the $[111]$-direction harbors an intermediate gapless quantum spin liquid (QSL) phase sandwiched between a gapped non-abelian QSL at low fields $H< H_{c1}$ and a partially polarized phase at high fields $H> H_{c2}$. Here, we analyze the low field and high field phases and phase transitions in terms of single- and two-magnon excitations using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods. We find that the energy to create a bound state of two-magnons $\Delta_p$ becomes lower than the energy to create a single spin flip $\Delta_s$ near $H_{c2}$. In the entire Kitaev spin liquid $\Delta_p<\Delta_s$ and both gaps vanish at $H_{c2}$. We make testable predictions for magnon pairing that could be observable in Raman scattering measurements on Kitaev QSL candidate materials.

Emergent Adler-Bardeen theorem

We consider a QEDd+1, d = 1, 3 lattice model with emergent Lorentz or chiral symmetry, both when the interaction is irrelevant or marginal. While the correlations present symmetry breaking corrections, we prove that the Adler-Bardeen (AB) non-renormalization property holds at a non-perturbative level even at finite lattice: all radiative corrections to the anomaly are vanishing. The analysis uses a new technique based on the combination of non-perturbative regularity properties obtained by exact renormalization Group methods and Ward Identities. The AB property, essential for the renormalizability of the standard model, is therefore a robust feature imposing no constraints on possible symmetry breaking terms, at least in the class of lattice models considered.

Current phases in Hofstadter ladder with staggered hopping

Hofstadter ladder describes a Boson ladder under a uniform magnetic field and supports nontrivial energy band and fractional quantum Hall states. Staggered hopping is illuminated from the SSH model and proved to have non-trivial effects on current phases. We introduce staggered hopping on Hofstadter ladder to study the novel current phases. Exact diagonalization (ED) and density matrix renormalization group (DMRG) methods have been employed to study the current phases of the ladder in noninteraction and strong interaction (hard core boson) cases. By observing energy singularities and the new flux patterns when increasing the staggered hopping strength, we extend Meissner and vortex phase to horizontal current phase, vertical current phase and vortex phase. The horizontal current phase has stronger chiral currents in horizontal direction, which is the long direction of the ladder. The vertical current phase has stronger chiral currents in vertical direction. The above two phases do not break translational invariance while the vortex phase does. The current patterns of horizontal current phase are proved to be continuously deformed form the Meissner phase, and the vortex phase has similar signatures. The vertical current phase is only visible when the hopping is staggered. These phases generally exist in noninteraction regimes and interacting superfluid regimes. We have defined new quantities (i.e. current inhomogeneity and nearest overlap) to characterize different quantum phases. In noninteraction case, the horizontal current phase go through the vortex phase to enter the vertical current phase by second order phase transitions, but in strong interaction case such a change can be directly made in a first order phase transition. The direct transition is made in higher fillings with almost identical flux. Surprisingly, the three phases turn into only two phases in Mott regimes, and the phase transition between the horizontal current phase and the vertical current phase has disappeared. We call the new phase as Mott-homogenous phase. The staggered hopping has exotic effects in strong interaction case. For &lt;i&gt;n&lt;/i&gt; = 0.25 filling, the staggered hopping shrinks the region of vortex phases and produces Mott-SF transition. When the staggered hopping is weak, the system achieves Mott-SF transition just by varying the flux. This research can enrich current phases in lattice systems and illuminate further studies on chiral currents.

Influence of applied electric and magnetic fields on a thermally-induced reentrance of a coupled spin-electron model on a decorated square lattice

The combination of an exact and Corner Transfer Matrix Renormalization Group (CTMRG) methods is used to study an influence of external electric and magnetic fields on existence of intriguing reentrant magnetic transitions in a coupled spin-electron model on a decorated square lattice. The two-dimensional (2D) decorated square lattice with localized nodal spins and delocalized electrons is taken into account. It was found that the competition among all involved interactions (the electron hopping, spin-spin and spin-electron interaction, external electric and magnetic fields) in combination with thermal fluctuations can produce new type of reentrant magnetic transitions. Depending on the model parameters the non-zero fields can stabilize or destabilize magnetic reentrance. In addition, an alternative and more effective way, for modulating the magnetic reentrance is found. An origin of intriguing low-temperature round maximum in the specific heat was explained as a consequence of rapid changes in the sublattice magnetizations, which is induced through a competition of all presented interactions.

Nonlocal string order parameter in the S=12 Kitaev-Heisenberg ladder

We study the spin-$\frac{1}{2}$ Kitaev-Heisenberg (KJ) model in a two-leg ladder. Without a Heisenberg interaction, the Kitaev phase in the ladder model has Majorana fermions with local Z$_2$ gauge fields, and is usually described as a disordered phase without any order parameter. Here we prove the existence of a non-local string order parameter (SOP) in the Kitaev phase which survives with a finite Heisenberg interaction. The SOP is obtained by relating the Kitaev ladder, through a non-local unitary transformation, to a one-dimensional $XY$ chain with an Ising coupling to a dangling spin at every site. This differentiates the Kitaev phases from other nearby phases including a rung singlet. Two phases with non-zero SOP corresponding to ferromagnetic and antiferromagnetic Kitaev interactions are identified. The full phase diagram of the KJ ladder is determined using exact diagonalization and density matrix renormalization group methods, which shows a striking similarity to the KJ model on a two-dimensional honeycomb lattice.

On the cutoff identification and the quantum improvement in asymptotically safe gravity

Applying the exact renormalization group method to search the non–Gaussian fixed points of gravitational coupling, is frequently followed by two steps: cutoff identification and improvement. Although there are various models for identifying the cutoff momentum by some physical length, saving the general covariance should be considered as an important property in the procedure. In this paper, use of an arbitrary function of curvature invariants for cutoff identification is suggested. It is shown that the field equations for this approach differs from the ones obtained from the conventional cutoff identification and improvement, even for non–vacuum solutions of the improved Einstein equations. Indeed, it is concluded that these two steps are correlated to each other.

Hidden spin current in doped Mott antiferromagnets

We investigate the nature of doped Mott insulators using exact diagonalization and density matrix renormalization group methods. Persistent spin currents are revealed in the ground state, which are concomitant with a nonzero total momentum or angular momentum associated with the doped hole. The latter determines a nontrivial ground state degeneracy. By further making superpositions of the degenerate ground states with zero or unidirectional spin currents, we show that different patterns of spatial charge and spin modulations will emerge. Such anomaly persists for the odd numbers of holes, but the spin current, ground state degeneracy, and charge/spin modulations completely disappear for even numbers of holes, with the two-hole ground state exhibiting a d-wave symmetry. An understanding of the spin current due to a many-body Berry-like phase and its impact on the momentum distribution of the doped holes will be discussed.

Heisenberg–Ising delta-chain with bond alternation

The spin- delta-chain (sawtooth chain) with antiferromagnetic Heisenberg basal chain and Ising apical-basal interactions is studied. The basal-apical interactions involve the bond alternation. The limiting cases of the model include the symmetrical delta-chain and the antiferromagnetic chain in the staggered magnetic field. We study ground state properties of the model by the exact diagonalization and density matrix renormalization group methods. The ground state phase diagram as a function of the bond alternation consists of magnetic and various non-magnetic phases. All phases excluding the ferrimagnetic phase are gapped and an origin of the gaps is cleared.

Universal Edge Transport in Interacting Hall Systems

We study the edge transport properties of $2d$ interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin-charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof.

Spin Hall insulators beyond the helical Luttinger model

We consider the interacting, spin conserving, extended Kane-Mele-Hubbard model, and we rigorously establish the exact quantization of the edge spin conductance and the validity of the Helical Luttinger liquid relations for Drude weights and susceptibilities. Our analysis fully takes into account lattice effects, typically neglected in the Helical Luttinger model approximation, which play an essential role for universality. The analysis is based on exact renormalization group methods and on a combination of lattice and emergent Ward identities, which allow to relate the emergent chiral anomaly with the finite renormalizations due to lattice corrections.