# Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

@article{Najafi2019FormationPA, title={Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains}, author={M N Najafi and Morteza Rajabpour}, journal={Physical Review B}, year={2019} }

We show that the computation of formation probabilities (FP) in the configuration basis and the full counting statistics (FCS) of observables in the quadratic fermionic Hamiltonians are equivalent to the calculation of emptiness formation probability (EFP) in the Hamiltonian with a defect. In particular, we first show that the FP of finding a particular configuration in the ground state is equivalent to the EFP of the ground state of the quadratic Hamiltonian with a defect. Then, we show that…

## 12 Citations

### Scaling of the formation probabilities and universal boundary entropies in the quantum XY spin chain

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

We calculate exactly the probability to find the ground state of the XY chain in a given spin configuration in the transverse σz-basis. By determining finite-volume corrections to the probabilities…

### Entanglement entropy in quantum spin chains with broken parity number symmetry

- PhysicsSciPost Physics
- 2022

Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is…

### Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

In this paper, we study the localized states of a generic quadratic fermionic chain with finite-range couplings and an inhomogeneity in the hopping (defect) that breaks translational invariance. When…

### Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain.

- PhysicsPhysical review. E
- 2021

By determining subleading corrections in a large interval asymptotics, the applicability of conformal field theory predictions at criticality is tested, and a universal interpolation formula is derived based on the solution of a Painlevé V equation for the full counting statistics of the transverse magnetization and the domain walls.

### Universal logarithmic correction to R\'enyi (Shannon) entropy in generic systems of critical quadratic fermions

- Computer Science
- 2022

This paper numerically calculate the R´enyi (Shannon) entropy in conﬁguration basis for wide variety of these models and shows that there are two distinct classes, and by using the discrete version of Bisognano-Wichmann modular Hamiltonian of the Ising chain it is shown that these coeﬃcients are universal and dependent on the underlying CFT.

### Universal logarithmic correction to R´enyi (Shannon) entropy in general critical quadratic fermions

- Physics
- 2022

The R´enyi (Shannon) entropy, i.e. Re α ( Sh ), of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at critical point there is…

### Quantum correlations in spin chains

- Physics
- 2020

The growth in the demand for precisely crafted many-body systems of spin-$1/2$ particles/qubits is due to their top-notch versatility in application-oriented quantum-enhanced protocols and the…

### Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

- Physics
- 2020

We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up,…

### Full counting statistics in the gapped XXZ spin chain

- PhysicsEPL (Europhysics Letters)
- 2020

We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse…

### Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium

- Physics
- 2020

We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a…

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