Related papers: Uncomputability of Phase Diagrams
We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb…
We determine the ground-state phase-diagram of a Hubbard Hamiltonian with correlated hopping, which is asymmetric under particle-hole transform. By lowering the repulsive Coulomb interaction U at appropriate filling and interaction…
Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its…
Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for…
In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model.…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
The form of the entanglement Hamiltonian varies with the parameters of the original system. Whether there is a singularity is the key problem for demonstrating/negating the universality of the relation between the entanglement spectrum and…
Parametric timed automata (PTAs) are a powerful formalism to reason, simulate and formally verify critical real-time systems. After 25 years of research on PTAs, it is now well-understood that any non-trivial problem studied is undecidable…
We prove quantitative decay estimates of macroscopic quantities generated by the solutions to linear transport equations driven by a general family of Hamiltonians. The associated particle trajectories are all trapped in a compact region of…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
The question of open-loop control in the Gaussian regime may be cast by asking which Gaussian unitary transformations are reachable by turning on and off a given set of quadratic Hamiltonians. For compact groups, including finite…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…