Related papers: Bootstrapping the gap in quantum spin systems
The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data…
Quantum phase transitions driven by electronic correlations are central to understanding the physics of graphene and related two-dimensional materials. A paradigmatic example is the semimetal-to-Mott-insulator transition on the honeycomb…
We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which…
The accurate computational determination of chemical, materials, biological, and atmospheric properties has critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
We describe the volume dependence of matrix elements of local boundary fields to all orders in inverse powers of the volume. Using the scaling boundary Lee-Yang model as testing ground, we compare the matrix elements extracted from boundary…
We incorporate the microscopic assumptions that lead to a certain generalization of the Lieb-Schultz-Mattis (LSM) theorem for one-dimensional spin chains into the conformal bootstrap. Our approach accounts for the "LSM anomaly" possessed by…
We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of…
Solving inverse problems to identify Hamiltonians with desired properties holds promise for the discovery of fundamental principles. In quantum systems, quantum entanglement plays a pivotal role in not only characterizing the quantum nature…
The purpose of the "bootstrap program" is to construct integrable quantum field theories in 1+1 dimensions in terms of their Wightman functions explicitly. As an input the integrability and general assumptions of local quantum field…
The purpose of the ``bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the…
Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo…
The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to…