Publications

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Engineering unique localization transition with coupled Hatano-Nelson chains

Ritaban Samanta, Aditi Chakrabarty, Sanjoy Datta

SciPost Phys. Core 8, 033 (2025) · published 27 March 2025 | · pdf

The paradigmatic Hatano-Nelson (HN) Hamiltonian induces a delocalization-localization (DL) transition in a one-dimensional (1D) lattice with random disorder, in striking contrast to its Hermitian counterpart. The DL transition also persists in the presence of a quasiperiodic potential separating completely delocalized and localized eigenstates. In this study, we reveal that coupling two 1D quasiperiodic Hatano-Nelson (QHN) lattices signiﬁcantly alters the nature of the DL transition and identify two critical points, $V_{c1} < V_{c2}$, when the nearest neighbors of the two 1D QHN lattices are cross-coupled with strong hopping amplitudes under periodic boundary conditions (PBC). Complete delocalization occurs below $V_{c1}$ and the states are completely localized above $V_{c2}$, while two mobility edges symmetrically emerge about Re[E] = 0 between $V_{c1}$ and $V_{c2}$. Notably, under speciﬁc asymmetric cross-hopping amplitudes, $V_{c1}$ approaches zero, resulting in localized states even for an inﬁnitesimally weak potential. Remarkably, we also ﬁnd that the mobility edges precisely divide the delocalized and localized states in equal proportions. We demonstrate a possible implementation of these findings in a coupled waveguided array which can be exploited to control and manipulate the light localization depending upon the hopping amplitude in the two QHN chains.

1 citation
Neural quantum state study of fracton models

Marc Machaczek, Lode Pollet, Ke Liu

SciPost Phys. 18, 112 (2025) · published 28 March 2025 | · pdf

Fracton models host unconventional topological orders in three and higher dimensions and provide promising candidates for quantum memory platforms. Understanding their robustness against quantum fluctuations is an important task but also poses great challenges due to the lack of efficient numerical tools. In this work, we establish neural quantum states (NQS) as new tools to study phase transitions in these models. Exact and efficient parametrizations are derived for three prototypical fracton codes — the checkerboard and X-cube model, as well as Haah's code — both in terms of a restricted Boltzmann machine (RBM) and a correlation-enhanced RBM. We then adapt the correlation-enhanced RBM architecture to a perturbed checkerboard model and reveal its strong first-order phase transition between the fracton phase and a trivial field-polarizing phase. To this end, we simulate this highly entangled system on lattices of up to 512 qubits with high accuracy, representing a cutting-edge application of variational neural-network methods. In addition, we reproduce the phase transition of the X-cube model previously obtained with quantum Monte Carlo and high-order series expansion methods. Our work demonstrates the remarkable potential of NQS in studying complicated three-dimensional problems and highlights physics-oriented constructions of NQS architectures.

1 citation
Quantum-inspired tempering for ground state approximation using artificial neural networks

Tameem Albash, Conor Smith, Quinn Campbell, Andrew D. Baczewski

SciPost Phys. 14, 121 (2023) · published 19 May 2023 | · pdf

A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.

1 citation
Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

Yang Gao, Phillip Helms, Garnet Kin-Lic Chan, Edgar Solomonik

SciPost Phys. Codebases 10 (2023) · published 24 February 2023 | · pdf

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

1 citation
Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling

Jan T. Schneider, Atsushi Ueda, Yifan Liu, Andreas M. Läuchli, Masaki Oshikawa, Luca Tagliacozzo

SciPost Phys. 18, 142 (2025) · published 29 April 2025 | · pdf

We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix's gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory (CFT). This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidence from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.

1 citation
Three-dimensional quantum Hall effect in topological amorphous metals

Jiong-Hao Wang, Yong Xu

SciPost Phys. 18, 146 (2025) · published 2 May 2025 | · pdf

Weyl semimetals have been theoretically predicted to become topological metals with anomalous Hall conductivity in amorphous systems. However, measuring the anomalous Hall conductivity in realistic materials, particularly those with multiple pairs of Weyl points, is a significant challenge. If a system respects time-reversal symmetry, then the anomalous Hall conductivity even vanishes. As such, it remains an open question how to probe the Weyl band like topology in amorphous materials. Here, we theoretically demonstrate that, under magnetic fields, a topological metal slab in amorphous systems exhibits three-dimensional quantum Hall effect, even in time-reversal invariant systems, thereby providing a feasible approach to exploring Weyl band like topology in amorphous materials. We unveil the topological origin of the quantized Hall conductance by calculating the Bott index. The index is carried by broadened Landau levels with bulk states spatially localized except at critical transition energies. The topological property also results in edge states localized at distinct hinges on two opposite surfaces.

1 citation
Spatial separation of spin currents in transition metal dichalcogenides

Antonio L. R. Manesco, Artem Pulkin

SciPost Phys. Core 6, 036 (2023) · published 1 May 2023 | · pdf

We theoretically predict spatial separation of spin-polarized ballistic currents in transition metal dichalcogenides (TMDs) due to trigonal warping. We quantify the effect in terms of spin polarization of charge carrier currents in a prototypical 3-terminal ballistic device where spin-up and spin-down charge carriers are collected by different leads. We show that the magnitude of the current spin polarization depends strongly on the charge carrier energy and the direction with respect to crystallographic orientations in the device. We study the (negative) effect of lattice imperfections and disorder on the observed spin polarization. Our investigation provides an avenue towards observing spin discrimination in a defect-free time reversal-invariant material.

1 citation
Effect of the Coulomb repulsion and oxygen level on charge distribution and superconductivity in the Emery model for cuprates superconductors

Louis-Bernard St-Cyr, David Sénéchal

SciPost Phys. Core 8, 043 (2025) · published 5 June 2025 | · pdf

The Emery model (aka the three-band Hubbard model) offers a simplified description of the copper-oxide planes that form the building blocks of high-temperature superconductors. By contrast with the even simpler one-band Hubbard model, it differentiates between copper and oxygen orbitals and thus between oxygen occupation ($n_p$) and copper occupation ($n_d$). Here we demonstrate, using cluster dynamical mean field theory, how the two occupations are related to the on-site Coulomb repulsion $U$ on the copper orbital and to the energy difference $\epsilon_p$ between oxygen and copper orbitals. Since the occupations ($n_p$ and $n_d$) have been estimated from NMR for a few materials (LCO, YBCO and NCCO), this allows us to estimate the value of $U-\epsilon_p$ for these materials, within this model. We compute the density of states for these and the effect of $(U,\epsilon_p)$ on the $n_d$-$n_p$ curve, superconductivity, and antiferromagnetism.

1 citation
Geometric constructions of generalized dual-unitary circuits from biunitarity

Michael A. Rampp, Suhail A. Rather, Pieter W. Claeys

SciPost Phys. 18, 182 (2025) · published 10 June 2025 | · pdf

We present a general framework for constructing solvable lattice models of chaotic many-body quantum dynamics with multiple unitary directions using biunitary connections. We show that a network of biunitary connections on the kagome lattice naturally defines a multi-unitary circuit, where three 'arrows of time' directly reflect the lattice symmetry. These models unify various constructions of hierarchical dual-unitary and triunitary gates and present new families of models with solvable correlations and entanglement dynamics. Using multilayer constructions of biunitary connections, we additionally introduce multilayer circuits with monoclinic symmetry and higher level hierarchical dual-unitary solvability and discuss their (non-)ergodicity. Our work demonstrates how different classes of solvable models can be understood as arising from different geometric structures in spacetime.

1 citation
Simulation of the 1d XY model on a quantum computer

Marc Farreras, Alba Cervera-Lierta

SciPost Phys. Lect. Notes 95 (2025) · published 11 June 2025 | · pdf

The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of $n=4$ and $n=8$ spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.

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