相关论文: Complexity and information geometry in spin chains

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…

The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its…

We propose a scheme for parameter estimation with the steady states of non-Hermitian spin chains. The parameters to be estimated are encoded in the system via the external magnetic field that imposed on the first site of the chain. We…

We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent…

We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional…

We show that the computational effort for the numerical solution of fermionic quantum systems, occurring e.g., in quantum chemistry, solid state physics, field theory in principle grows with less than the square of the particle number for…

We measure the density profiles for a Fermi gas of $^6$Li containing $N_1$ spin-up atoms and $N_2$ spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin-imbalance $N_2/N_1$…

We consider the partial transpose of the spin reduced density matrix of two disjoint blocks in spin chains admitting a representation in terms of free fermions, such as XY chains. We exploit the solution of the model in terms of Majorana…

The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…

The spin-fermion model has long been used to describe the quantum-critical behavior of 2d electron systems near an antiferromagnetic (AFM) instability. Recently, the standard procedure to integrate out the fermions to obtain an effective…

We show that a quantum spin system has an exact description by non-interacting fermions if its frustration graph is claw-free and contains a simplicial clique. The frustration graph of a spin model captures the pairwise anticommutation…

We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…

Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…

We consider random transverse-field Ising spin chains and study the magnetization and the energy-density profiles by numerically exact calculations in rather large finite systems ($L\le 128$). Using different boundary conditions (free,…

There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…

We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic critical point. We show how the critical spin fluctuations at the AFM wavevector q=Q…

We introduce a new a family of $Z(N)$ multispins quantum chains with a free-fermionic ($N=2$) or free-parafermionic ($N>2$) eigenspectrum. The models have $(p+1)$ interacting spins ($p=1,2,\dots$), being Hermitian in the $Z(2)$ (Ising) case…

We introduce a notion of s-holomorphicity suitable for certain quantum spin systems in one dimension, and define two observables in the critical transverse-field Ising model which have this property. The observables are defined using…

The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure…