One Dimension, Countless Directions

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I will describe a simple derivation of the integrability of the XYZ chain with nary an elliptic function in sight. The key is to write the strong zero mode in terms of a matrix-product operator. It then becomes easy to generalise this operator to yield a sequence of charges commuting with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A less simple but straightforward calculation yields three-spin interactions that may be spatially varying without destroying the integrability, and placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk (work w/ S. Gehrmann, E. Vernier and F. Verstraete).

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We consider the quantum integrable spin chain models based on the quantum affine algebra $D^{(2)}_{n+1}$ subject to twisted periodic and quantum-group-invariant open boundary conditions. For $n=1$ it has been established that, depending on the choice of boundary conditions, the low energy physics of the model is described either by a non-compact (boundary) CFT related to the 2D black hole sigma model in a range of anisotropies or a CFT with purely discrete spectrum of conformal weights. In this talk, we present results of joint recent work with Sascha Gehrmann, Rafael Nepomechie and Ana Retore on the continuum limit of the $D^{(2)}_{3}$ model.

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Form factor series for the dynamical two-point correlation functions of the Lieb-Liniger model at generic coupling c > 0 can be interpreted as being generated by the action of certain ‘functional translation operators’ on series that resemble those obtained in the infinite coupling limit and take the form of Fredholm determinants or Fredholm minors, but with a number of ‘functional parameters’, on which the functional translation operators can act, included. The Fredholm determinants and minors appearing in this context involve so-called integrable operators. Their long-time large-distance asymptotics can be studied by means of the non-linear steepest descent method. We have solved the underlying matrix Riemann-Hilbert problem for the finite-temperature case, respectively for equlibrium states parameterized by a certain class of filling fractions. Acting with the appropriate functional translation operator on the asymptotic expressions for the Fredholm determinants and minors will give the asymptotics of the corresponding correlation functions of the Lieb-Liniger model in the finite-c case. As a first step on this way we have revisited the analysis of the field-field correlation functions and have amended, corrected and simplified the 1992 result of Its, Izergin, Korepin and Varzugin.

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We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, $\sigma_n^x$ and $\sigma_n^y$, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.

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I will present experimental results for the implementation of dynamics of the Hubbard model on a 6x6 square lattice, using 90 qubits, on Quantinuum Helios ion-trap quantum computer. This will include in particular results of a free-fermion benchmark protocol and of a light-induced superconductivity experiment, inspired from previous studies on the one-dimensional Hubbard model. I will discuss the octagon fermionic encoding used and will address the question of the simulability of the circuits run on hardware.

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It is shown that the Ruderman-Kittel-Kasua-Yoisida interaction between overscreened spins in two channel Kondo impurity systems is a relevant perturbation when the number of impurities N is greater than 3 driving the system to a new quantum critical point with anomalous dimensions 1 (N +1) 3 for the spin operator and the Sommerfeld coefficient of the specific heat scales as γ∼ T− N+1 . The critical point universal properties are relevant to many strong correlation problems, such as impurity placed in a Majorana metal and the multichannel Kondo lattice model of heavy fermion materials. We discuss relevance of our results for cluster DMFT studies of quantum criticality.

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We reconsider the problem of using form factor expansions at finite temperature to compute the Drude weight in the sine-Gordon model. We find a dichotomy between the Drude weight at the model’s reflectionless points and where scattering is non-diagonal. At the reflectionless points, the form factor expansion appears to be regular order by order and agrees with the prediction of generalized hydrodynamics (GHD). Away from these points, the form factor expansion takes on the character of a short time expansion where the current-current correlation sees divergences at each order. These divergences can be resummed however, at least if only the leading divergences at each order are accounted for. We comment on how this might be connected to the fractal structure of the Drude weight predicted by GHD.

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At high temperatures, quantum effects are generally considered unimportant, giving way to classical behavior. In magnetic systems, when thermal energies exceed the interaction strength between atomic magnetic moments, the spins typically become uncorrelated, resulting in classical paramagnetism. This thermal decoherence of quantum spins is a major hindrance to quantum information applications of spin systems. Remarkably, our neutron scattering experiments on Yb chains in an insulating perovskite crystal defy these conventional expectations [1]. Specific origin of effective quantum spins describing the ground crystal field doublet of Yb J=7/2 spin-orbital multiplet affords an opportunity to study excitations at temperatures much greater than spin interactions. It also provides remarkable sensitivity to specific entangled quantum spin states. We observe a sharply defined spinon continuum, a hallmark of fractionalized excitations in one-dimensional quantum magnets, persisting to temperatures well above the energy scale of Yb-Yb interactions. The observed sharpness of the spinon continuum’s dispersive upper boundary indicates a spinon mean free path exceeding ≈ 35 inter-atomic spacings at temperatures more than an order of magnitude above the interaction energy scale. By Fourier transforming the measured dynamical spin susceptibility we obtain a real space-time linear response function which allows direct measurement of the spinon propagation velocity both at low and high temperature, which provides direct experimental probe of asymptotic freedom of strongly interacting one-dimensional fermions.

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The transition probability of the ASEP on the half line with general, non-particle-conserving open boundaries can be derived using the (stochastic) six vertex model. The empty-to-empty transition probability is non-trivial due to particles in the system at intermediate times, but the simplest quantity while retaining non-trivial features of generic non-diagonal boundaries. I will further discuss a Pfaffian structure for the general transition probability in the TASEP limit.

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I will discuss a fascinating example of exactly solvable reversible cellular automaton in 1+1 dimensions, the rule 54, and two of its deformations which turn the model into either quantum or stochastic cellular automaton. The (deformed) model can be interpreted as arguably the simplest integrable dynamics with interaction round-a-face. Both deformations, being parametrixed by an arbitrary unitary or stochastic 2x2 matrix, respectively, exhibit some features of integrability. The later (stochastic version) can be interpeted as a lattice discretization of deformed t-PNG model. I will discuss the construction of non-trivial conservation laws of the quantum deformation and the matrix product form of the steady state of the boundary driven stochastic deformation. If time permits, I will also mention a certain 2+1 dimensional deterministic extention exibiting robust soliton scattering and rich manifold of strongly correlated time-translation invariant states.

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Quantum spin systems provide tabletop realizations of deeply entangled quantum states. They have been central both in validating field theories in condensed matter physics and in inspiring new computational approaches. Today, they are emerging as testbeds for quantum simulators and quantum computers. Neutron scattering remains the most powerful technique for directly probing these quantum states, offering unique insight into their structure and dynamics. In this talk, I will highlight recent breakthroughs from neutron experiments on one- and two-dimensional materials, both in and out of equilibrium.

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The antiferromagnetic spin-1/2 spin chain with Heisenberg-Ising (XXZ) anisotropy is a rich source of novel phenomena. Good physical realizations are the compounds SrCo2V2O8 and BaCo2V2O8 where the Co2+ ions have effective spin-1/2 and are coupled by antiferromagnetic interactions into chains while collinear long-range magnetic order occurs below TN ~ 5 K due to weak interchain coupling. In a longitudinal magnetic field applied along the easy axis, the magnetic order is suppressed and using inelastic neutron scattering and optical spectroscopy we find the evidence for complex bound states of magnetic excitations, known as Bethe strings. Furthermore, the characteristic energy, scattering intensity and linewidth of the observed string states exhibit excellent agreement with precise Bethe ansatz calculations. Our results confirm the existence of the long-sought Bethe string excitations predicted almost a century ago. Application of transverse magnetic field along the direction perpendicular to the easy axis induces a quantum phase transition where the antiferromagnetic order is destroyed at a three-dimensional quantum critical point. The evolution of the excitations is investigated as a function of field revealing a complex series of modes and continuua. At a particular field still within the antiferromagnetically ordered phase we find a sequence of excitations whose energies match the lightest three E8 particles corresponding to the maximal exceptional Lie E8 algebra.

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One dimensional systems are an interesting playground for many body physics and its emerging Descriptions. One is in form of emerging Quantum Field Theories (QuFT) with bosonic excitations. These range from, in their simplest form, a Bosonic Luttinger Liquid supporting phonons, to the description of two tunnel coupled 1d quantum liquids as a strongly correlated topological Sine Gordon QuFT [1]. The other very powerful description is through generalized Hydrodynamics, which is based on the Bethe Ansatz solution of the Lieb-Liniger model and supports rapidities which have Fermionic statistics. In my talk I will contrast the two descriptions through their experimental consequences, the emergence of Fermionic Pauli blocking in a weakly interacting Bose gas [3] and its consequence of preserving near integrability behaviour far beyond what would normally be expected. Finally I will reconcile the two descriptions by a detailed measurements of phonon lifetimes and their scaling [3]. Work Supported by the DFG-FWF SFB ISOQUANT, and the ERC-AdG Emergence in Quantum Physcs (EmQ) [1] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126 [2] F. Cataldini et al. Phys. Rev. X 12, 041032 (2022). [3] F. Cataldini et al. In preparation (2025)

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The propagation of wave packets with unit charge provides valuable information about the dispersion relation of elementary particles. In strongly correlated systems that exhibit charge fractionalization, one expects a single wave packet to split into multiple parts that carry fractional charges. In this talk I will discuss the time evolution in a critical fermionic chain starting from an initial state where a Gaussian wave packet is prepared with arbitrary momentum, not restricted to the low-energy limit. I will show that the dynamics is well described by nonlinear Luttinger liquid theory, and the fractional charges observed in real time provide a direct measurement of interaction parameters that govern various threshold singularities of dynamic response functions in the frequency domain. Moreover, at high energies, the evolution of a wave packet with unit charge reveals signatures of composite excitations containing two-particle bound states.