Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.12357

Cluster-projected matrix product state: framework for engineering exact quantum many-body ground states in one and two dimensions

Hidehiro Saito·Chisa Hotta
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product state (MPS) representation. Our approach strategically chooses a local cluster Hamiltonian, which is arranged to overlap with neighboring clusters on a designed lattice. The frustration-free Hamiltonian is given as the sum of the cluster Hamiltonians by ensuring that there exists a state that has its local submanifolds as the lowest-energy eigenstate of every cluster. The key to find such a solution is a systematic protocol, which projects out excited states on every cluster using MPS and effectively entangles the cluster states. The protocol offers several advantages, including the ability to achieve exact many-body ground-state solutions at nearly equal cost in one and two dimensions, those belonging to gapless or long-range entangled classes of ground states, flexibility in designing Hamiltonians unbiasedly across various forms of models, and numerically feasible validation through energy calculations. Our protocol offers the exact ground state for general frustration-free Hamiltonian, and enables the exploration of exact phase boundaries and the analysis of even a spatially nonuniform random system, providing platforms for quantum simulations and benchmarks.

Explore related subjects

cond-mat.str-el

Keep this discovery

BibTeXRIS

Hidehiro Saito, Chisa Hotta. 2024-06-18. Cluster-projected matrix product state: framework for engineering exact quantum many-body ground states in one and two dimensions. https://arxiv.org/abs/2406.12357

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competing Interlayer Loop Currents and Superconductivity in the Bilayer $t$-$J_\perp$-$V$ Model

The recent discovery of high-$T_c$ superconductivity in pressurized and thin-film bilayer nickelates, featuring a strong interlayer exchange coupling, and their potential similarities with cuprate superconductors, has made this a very active topic in condensed matter physics. In the present paper we study the strongly correlated one-orbital ($d_{x^2-y^2}$) bilayer $t$-$J_\perp$-$V$ model for nickelates, where $V$ denotes the Coulomb interactions, using a controlled large-$N$ expansion at and beyond the mean-field level. Focusing on the out-of-plane spin exchange interaction ($J_\perp$), we find that it triggers both out-of-plane $s$-wave superconductivity and an out-of-plane bond-order phase ($z$-BOP) instability. The $z$-BOP gives rise to a complex $z$-axis hopping dominated by its imaginary component, which drives out-of-plane currents and induces in-plane ones, spontaneously forming on the vertical plaquettes a loop-current state that breaks time-reversal symmetry. Competition between this loop-current phase and superconductivity yields a dome-shaped superconducting region, with optimal superconductivity occurring near the $z$-BOP quantum critical point. The resulting phase diagram features a pure loop-current region, a low-doping coexistence phase, a pure superconducting state at higher doping, and a correlated metallic state.

cond-mat.str-el↗
arXiv2026

Optically induced metallic state with persistent monoclinic symmetry in NdNiO$_3$

Understanding whether electronic and structural order remain coupled under nonequilibrium conditions is a central challenge in correlated materials. Here, we simultaneously track metallicity and symmetry across the photoinduced insulator-to-metal transition in NdNiO$_3$ using time-resolved optical reflectivity and symmetry-sensitive second-harmonic generation. We find that metallic reflectivity emerges at significantly lower excitation fluence than restoration of the orthorhombic high-temperature symmetry. As a result, optical excitation stabilizes a metastable state that combines the reflectivity of the metallic phase with the monoclinic symmetry of the insulating phase, revealing an optically induced monoclinic metal. Only at substantially higher fluences does the symmetry fully recover to that of the high-temperature phase. These results demonstrate a nonequilibrium decoupling of metallicity and structural symmetry and establish simultaneous multiprobe spectroscopy as a powerful approach for identifying emergent phases in correlated materials.

cond-mat.str-el↗
arXiv2026

Instabilities in self-consistent diagrammatic approaches and how to cure them

While self-consistent diagrammatic approaches are widely used to compute the physical properties of correlated quantum materials, their applicability may get severely hindered precisely in the parameter regions, where the most exciting physics is observed. One of the major issues, referred to as "misleading convergence", is the tendency of iterative schemes to converge to unphysical fixed points for intermediate-to-strong electronic interactions, regardless of numerical accuracy of the computation. Here, we explicitly verify that the origin of this problem in several established self-consistent many-electron approaches, defined in the general diagrammatic framework of the boson-exchange formalism, resides exclusively in the stability condition of the respective iteration schemes, and not in an intrinsic breakdown of their self-consistent diagrammatic description. This insight enables a simple and general remedy, as recently proposed in Phys. Rev. Lett. 137, 016502 (2026): The redefinition of the iterative procedure, by inverting the unstable eigendirections of the Jacobian associated to the fixed point of the self-consistent algorithm. We illustrate the successful outcome of this procedure by means of systematic calculations performed on testbed, exactly solvable, models. Our results demonstrate that the physical fixed point of the diagrammatic schemes we considered can be stabilized, de facto, across the entire parameter range, including the most challenging nonperturbative/strong-coupling regimes.

cond-mat.str-el↗