We consider Gaussian quantum circuits that alternate unitary gates and postselected weak measurements, with spatial translation symmetry time p eriodicity. show analytically such models can host different kinds of measurement-induced phase transitions detected by entanglement entropy, mapping the measurements onto M\"obius transformations. demonstrate existence a log-law to area-law transition, as well volume-law transition at finite measurement amplitude. For latter, we compute critical...

We consider the problems of calculating dynamical order parameter two-point function at finite temperatures and one-point after a quantum quench in transverse field Ising chain. Both these can be expressed terms form factor sums basis physical excitations model. develop general framework for carrying out based on decomposition factors into partial fractions, which leads to factorization multiple permits them evaluated asymptotically. This naturally systematic low density expansions. At late...

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model arbitrary energy eigenstates and all space time, that combines Lehmann representation with 1/c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mi>/</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:math> expansion. The n^\mathrm{th} display="inline"><mml:msup><mml:mi>n</mml:mi><mml:mstyle...

We provide analytic, numerical, and experimental evidence that the amount of noise in digital quantum simulation local observables can be independent system size a number situations. microscopic explanation this based on “relevant string length” operators, which is length Pauli strings operator at time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>s</a:mi></a:math> belong to exponentially small subspace give nonzero expectation value <d:math...

It is well known that simulating quantum circuits with low but nonzero hardware noise more difficult than without noise. requires either to perform density matrix simulations (coming a space overhead) or sample over “quantum trajectories” where Kraus operators are inserted randomly runtime overhead). We propose simulation technique based on representation of in terms trajectories generated by remain close identity at give explicit expressions for can be represented Pauli channels, as certain...

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides natural unified framework for out-of-equilibrium physics in this model. show $all$ correlation functions CE can be computed using form factor expansion expressed terms Fredholm determinants. In particular, we present exact expressions thermodynamic limit previously unknown order parameter one-point...

The fraction of primordial black holes (PBHs) masses ${10}^{17}--{10}^{26}\text{ }\text{ }\mathrm{g}$ in the total amount dark matter may be constrained by considering their capture neutron stars (NSs), which leads to rapid destruction latter. constraints depend crucially on rate which, turn, is determined energy loss a PBH passing through NS. Two alternative approaches estimate have been used literature: one based dynamical friction mechanism, and another tidal deformations NS PBH. second...

We show that the variational quantum-classical simulation algorithm admits a finite circuit depth scaling collapse when targeting critical point of transverse field Ising chain. The order parameter only collapses on one side transition due to slowdown quantum crossing phase transition. In assess performance and compute correlations in system up 752 qubits, we use techniques from integrability derive closed-form analytical expressions for expectation values with respect output circuit. also...

We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. show that it is possible perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions densities these at second order higher are generally nonlocal become spatially localized only if potential fulfils certain compatibility conditions. prove solutions first conditions Cheon-Shigehara...

We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of functional that maps function to sum its evaluations over roots. A simple powerful constraint derived when applying this infinitely derivable test functions with compact support, generalizes then more general functions. The presented context spin-1/2 XXZ chain which we derive corrections leading eigenvalues Hamiltonian any configuration...

We consider the transverse field Ising model with additional all-to-all interactions between spins. show that a mean-field treatment of this becomes exact in thermodynamic limit, despite presence 1D short-range interactions. Namely, we eigenstates are coherent states an amplitude varies through Hilbert space, within which expectation values local observables can be computed theory. study then thermodynamics and identify different phases. Among its peculiar features, possesses second-order...

In one-dimensional quantum gases there is a well known "duality" between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting to weakly fermions known. Here we propose solution this long-standing problem. Our derivation relies on regularizing only pointlike interaction in one dimension that induces discontinuity wave function proportional its derivative. contrast all regularizations our potential weak for small...

We obtain the ground state magnetization of Heisenberg and XXZ spin chains in a magnetic field h as series , where hc is smallest for which fully polarized. All coefficients can be computed closed form through recurrence formula that involves only algebraic manipulations. For some values anisotropy parameter expansion numerically observed to convergent full range .

The six-vertex model with domain-wall boundary conditions is one representative of a class two-dimensional lattice statistical mechanics models that exhibit phase separation known as the arctic curve phenomenon. In thermodynamic limit, degrees freedom are completely frozen in region near boundary, while they critically fluctuating central region. separates those two regions. Critical fluctuations inside have been studied extensively, both physics and mathematics, free (i.e., map to fermions,...

A bstract We formulate Q -systems for the closed XXZ, open XXX and quantum- group-invariant XXZ quantum spin chains. Polynomial solutions of these can be found efficiently, which in turn lead directly to admissible corresponding Bethe ansatz equations.

A bstract We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges gap between different criteria, yielding an alternative proof of a recently devised algorithm based on QQ relations, and solving its minimality issue.

The tangent method has recently been devised by Colomo and Sportiello (2016 J. Stat. Phys. 164 1488–523) as an efficient way to determine the shape of arctic curves. Largely conjectural, it tested successfully in a variety models. However no proof general geometric insight have given so far, either show its validity or allow for understanding why actually works. In this paper, we propose universal framework which accounts tangency part method, whenever formulation terms directed lattice...

We derive explicit expressions for dynamical correlations of the field and density operators in Lieb-Liniger model, within an arbitrary eigenstate with a small particle ${\cal D}$. They are valid all space time any interaction strength $c>0$, leading order expansion This is obtained by writing correlation functions as sums over form factors when formally decomposed into partial fractions.

We consider the time evolution of local observables after an interaction quench in repulsive Lieb-Liniger model. The system is initialized ground state for vanishing and then time-evolved with Hamiltonian large, finite interacting strength $c$. employ Quench Action approach to express full terms sums over energy eigenstates derive leading a $1/c$ expansion several one two-point functions as function $t > 0$ quantum quench. observe delicate cancellations contributions spectral that depend on...

Two-dimensional sigma models on superspheres are known to flow weak coupling in the IR when r − 2s < 2. Their long-distance properties described by a free 'Goldstone' conformal field theory with 1 bosonic and fermionic degrees of freedom, where symmetry is spontaneously broken. This behavior made possible lack unitarity.

Abstract Pointlike interactions between bosons in 1D are related to pointlike fermions through the Girardeau mapping. This mapping is a strong–weak duality since coupling constants bosonic and fermionic cases inversely proportional each other. We present regularization of these that preserves duality, contrary previously known Hermitian regularizations. proven rigorously. allows one use this perturbatively we illustrate it Lieb–Liniger model at strong coupling.

It is generally considered that the signal output by a quantum circuit attenuated exponentially fast in number of gates. This letter explores how algorithms using mid-circuit measurements and classical conditioning as computational tools (and not error mitigation or correction subroutines) can be naturally resilient to complete decoherence, maintain states with useful properties even for infinitely deep noisy circuits. Specifically, we introduce channel built out feed-forward, used compute...

According to the adiabatic theorem of quantum mechanics, a system initially in ground state Hamiltonian remains if one slowly changes Hamiltonian. This can be used principle solve hard problems on computers. Generically, however, implementation this dynamics digital computers requires scaling Trotter step size with and simulation time, which incurs large gate count. In work, we argue that for classical optimization problems, evolution performed fixed, finite step. "Floquet evolution" reduces...