arXiv subjects

Johannes Motruk

Publications and source records attributed to Johannes Motruk.

At least 19 recordsLinked to original sources

arXiv2026

Precision quantum simulation of magnon spectra and interactions

Quantum simulation promises to advance materials discovery by accurately simulating complex states of matter, their microscopic excitations, and macroscopic response functions. The central challenge in resolving the underlying interacting dynamics is to combine high-fidelity evolution with the sophisticated control necessary to manipulate individual quasi-particles in quantum many-body states. Here, we report on high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits. By interleaving digital gates with analog evolution precisely characterized via Hamiltonian learning, we selectively excite magnons at tunable energy densities. Measuring first the linear magnon response -- a central probe in neutron-scattering experiments -- we extract temperature-dependent spectra and lifetimes. Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes. Next, we perform a suite of nonlinear measurements, including the study of self-scattering mechanisms, as well as pump-probe spectroscopy to directly characterize the magnon interactions. While matrix-product state simulations capture the dynamics well in either small systems or at low temperatures, their predictions become inaccurate away from these limits. This work demonstrates precise simulation of the interacting dynamics in quantum magnets, and provides key insights into quasi-particles and their microscopic scattering mechanisms.

quant-ph↗

arXiv2025

Fractional Chern insulator edges: crystalline effects and optical measurements

Edge states of chiral topologically ordered phases are commonly described by chiral Luttinger liquids, effective theories that are exact only in the hydrodynamic limit. Motivated by recent bulk observations of fractional Chern insulators (FCIs) in two-dimensional materials and by synthetic realizations in ultracold atoms, we revisit this framework and quantify deviations from the hydrodynamic limit due to lattice effects. Using a combination of analytical arguments and numerical simulations, we disentangle universal from nonuniversal edge properties. We outline experimental probes in excitonic FCIs and in ultracold atom systems, and in particular propose time-resolved edge spectroscopy to directly access the predicted exponents and velocities.

cond-mat.str-el↗

arXiv2025

Ground states of quasi-two-dimensional correlated systems via energy expansion

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasi-local interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin-$1/2$ Heisenberg Hamiltonian, and spinful fermions with repulsive interactions. In particular, we showcase a non-trivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion-framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion-framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.

cond-mat.str-el↗

arXiv2024

Thermalization and Criticality on an Analog-Digital Quantum Simulator

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

quant-ph↗

arXiv2024

Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group

We microscopically analyze the nearest neighbor Heisenberg model on the maple-leaf lattice through neural quantum states (NQS) and infinite density matrix renormalization group (iDMRG). Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling $J_d$ varied against the exchange strength $J$ of all other bonds, iDMRG (NQS) finds a dimer state paramagnetic phase for $J_d/J > 1.464$ ($J_d/J > 1.39$) and a canted $120^\circ$ magnetic order for $J_d/J < 1.419$ ($J_d/J < 1.23$). Assessing training convergence inaccuracies of NQS and the influence of finite cylindric circumference for iDMRG, we discuss the possible existence of an intermediate phase between magnet and dimer paramagnet.

cond-mat.str-el↗

arXiv2023

Kagome chiral spin liquid in transition metal dichalcogenide moiré bilayers

At $n=3/4$ filling of the moiré flat band, transition metal dichalcogenide moiré bilayers will develop kagome charge order. We derive an effective spin model for the resulting localized spins and find that its further neighbor spin interactions can be much less suppressed than the corresponding electron hopping strength. Using density matrix renormalization group simulations, we study its phase diagram and, for realistic model parameters relevant for WSe$_2$/WS$_2$, we show that this material can realize the exotic chiral spin liquid phase and the highly debated kagome spin liquid. Our work thus demonstrates that the frustration and strong interactions present in TMD heterobilayers provide an exciting platform to study spin liquid physics.

cond-mat.str-el↗

arXiv2021

Performance of the rigorous renormalization group for first order phase transitions and topological phases

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in 1D systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau et al. [Nature Physics 11, 566 (2015)]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first order phase transitions and in symmetry protected topological phases. Our study is motived by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near) degenerate manifolds. The rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines accurate, well-ordered energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.

cond-mat.str-el↗

arXiv2021

Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice

At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically relevant parameters, they stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

cond-mat.str-el↗

arXiv2021

Phase diagram of the anisotropic triangular lattice Hubbard model

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. When one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice Néel order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

cond-mat.str-el↗

arXiv2020

Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement

The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a $ν= 1/2$ FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity $σ_{xy}$ can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to $σ_{xy}$ for an extended range of field strengths.

cond-mat.quant-gas↗

arXiv2020

Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

cond-mat.str-el↗

arXiv2020

Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition

As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-André model at a finite disorder strength. On the single-particle level, many properties of the ground-state critical behavior have been revealed by applying a real-space renormalization-group scheme; the critical properties are determined solely by the continued fraction expansion of the incommensurate frequency of the disorder. Here, we investigate the many-particle localization-delocalization transition in the Aubry-André model with and without interactions. In contrast to the single-particle case, we find that the critical exponents depend on a Diophantine equation relating the incommensurate frequency of the disorder and the filling fraction which generalizes the dependence, in the single-particle spectrum, on the continued fraction expansion of the incommensurate frequency. This equation can be viewed as a generalization of the resonance condition in the commensurate case. When interactions are included, numerical evidence suggests that interactions may be irrelevant at at least some of these critical points, meaning that the critical exponent relations obtained from the Diophantine equation may actually survive in the interacting case.

cond-mat.stat-mech↗

arXiv2018

Charge excitation dynamics in bosonic fractional Chern insulators

The experimental realization of the Harper-Hofstadter model in ultra-cold atomic gases has placed fractional states of matter in these systems within reach---a fractional Chern insulator state (FCI) is expected to emerge for sufficiently strong interactions when half-filling the lowest band. The experimental setups naturally allow to probe the dynamics of this topological state, yet little is known about its out-of-equilibrium properties. We explore, using density matrix renormalization group (DMRG) simulations, the response of the FCI state to spatially localized perturbations. After confirming the static properties of the phase we show that the characteristic, gapless features are clearly visible in the edge dynamics. We find that a local edge perturbation in this model propagates chirally independent of the perturbation strength. This contrasts the behavior of single particle models with counter-propagating edge states, such as the non-interacting Harper-Hofstadter model, where the chirality is manifest only for weak perturbations. Additionally, our simulations show that there is inevitable density leakage from the first row of sites into the bulk, preventing a naive chiral Luttinger theory interpretation of the dynamics.

cond-mat.str-el↗

arXiv2017

Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162 (2015)] at half filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.

cond-mat.str-el↗

arXiv2016

Density matrix renormalization group on a cylinder in mixed real and momentum space

We develop a variant of the density matrix renormalization group (DMRG) algorithm for two-dimensional cylinders that uses a real space representation along the cylinder and a momentum space representation in the perpendicular direction. The mixed representation allows us to use the momentum around the circumference as a conserved quantity in the DMRG algorithm. Compared with the traditional purely real-space approach, we find a significant speedup in computation time and a considerable reduction in memory usage. Applying the method to the interacting fermionic Hofstadter model, we demonstrate a reduction in computation time by over 20-fold, in addition to a sixfold memory reduction.

cond-mat.str-el↗

arXiv2015

Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study

The emergence of the Haldane Chern insulator state due to strong short range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting i) the absence of the Chern insulator state, ii) two previously unnoticed charge ordered phases and iii) the existence and stability of all the non-topological competing orders that were found previously within mean field. In addition, we discuss the nature of the corresponding phase transitions based on our numerical data. Our work establishes the phase diagram of the half-filled honeycomb lattice model tilting the balance towards the absence of a Chern insulator phase for this model.

cond-mat.str-el↗

arXiv2015

Characterization and stability of a fermionic ν=1/3 fractional Chern insulator

Using the infinite density matrix renormalization group method on an infinite cylinder geometry, we characterize the $1/3$ fractional Chern insulator state in the Haldane honeycomb lattice model at $ν=1/3$ filling of the lowest band and check its stability. We investigate the chiral and topological properties of this state through (i) its Hall conductivity, (ii) the topological entanglement entropy, (iii) the $U(1)$ charge spectral flow of the many body entanglement spectrum, and (iv) the charge of the anyons. In contrast to numerical methods restricted to small finite sizes, the infinite cylinder geometry allows us to access and characterize directly the metal to fractional Chern insulator transition. We find indications it is first order and no evidence of other competing phases. Since our approach does not rely on any band or subspace projection, we are able to prove the stability of the fractional state in the presence of interactions exceeding the band gap, as has been suggested in the literature. As a by-product we discuss the signatures of Chern insulators within this technique.

cond-mat.str-el↗

arXiv2013

Topological phases in gapped edges of fractionalized systems

Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. We introduce a classification scheme for the phases that can occur in parafermionic chains. We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense. In the presence of additional symmetries, the phases form a non-Abelian group. As a concrete example of the classification, we consider the effective edge model for a $ν= 1/3$ fractional topological insulator for which we calculate the entanglement spectra numerically and show that all possible predicted phases can be realized.

cond-mat.str-el↗