Quantum phase transitions are characterized by the universal scaling laws in the critical region surrounding the transitions. This universality is also manifested in the critical real-time dynamics through the quantum Kibble- Zurek mechanism. In recent experiments on a Rydberg atom quantum simulator, the Kibble-Zurek mechanism was used to probe the nature of quantum phase transitions. In this paper, we analyze the caveats associated with this method and develop strategies to improve its accuracy. Focusing on two minimal models—transverse-field Ising and quantum three-state Potts, both in one dimension—we study the effect of boundary conditions, the location of the endpoints, and some subtleties in the definition of the kink operators. In particular, we show that the critical scaling of the most intuitive types of kinks is extremely sensitive to the correct choice of endpoint, while more advanced types of kinks exhibit remarkably robust universal scaling. Furthermore, we show that when kinks are tracked over the entire chain, fixed boundary conditions improve the accuracy of the scaling. Surprisingly, the Kibble-Zurek critical scaling appears to be equally accurate whether the fixed boundary conditions are chosen to be symmetric or antisymmetric. We also show that the density of kinks extracted in the central part of long chains obeys the predicted universal scaling for all types of boundary conditions. Finally, we test our kink definition for the Ising transition on the period-2 phase of the Rydberg model and show that it is more robust against the endpoint than the standard definition.

We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the ℤ₂-orbifold of the c = 1 compactified boson boundary conformal field theory, we construct microscopic lattice boundary terms that renormalize to the stable conformal boundary conditions, utilizing simple current extensions and the underlying SU(2) symmetry to explicitly characterize the four-state Potts point. We validate these theoretical identifications via finite-size spectroscopy of the lattice energy spectra, confirming their consistency with D₄ symmetry and Kramers-Wannier duality. Finally, we discuss the boundary renormalization group flows among these identified fixed points to propose a global phase diagram for the boundary criticality.

Using a combination of time-dependent density matrix renormalization group and single mode approximation, we investigate the dynamical structure factor of spin chains with antiferromagnetic nearest-neighbor J₁, next-nearest-neighbor J₂, and three-site J₃ interactions and show that, in all gapped phases and at the transitions between them, a simple physical picture can be obtained in terms of magnons and spin-1/2 domain-wall excitations or spinons. This applies to the fully dimerized phase, where a magnon mode clearly pops out of the two-spinon continuum for spin-1 and spin-3/2, and to the transition between the dimerized phase and the Haldane phase (resp. partially dimerized phase) for spin-1 (resp. spin-3/2), where spinons are deconfined along the transition but get confined across it when it is first order. Implications for the interpretation of inelastic neutron scattering in spin chains are briefly discussed.

We study the dynamical structure factor of the frustrated spin-3/2 J₁-J₂ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at J₂ ≈ 0.32J₁, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at J₂ ≈ 0.4J₁ beyond the Lifshitz point (J₂ ≈ 0.388J₁). The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-5/2 case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the noninteracting infinite randomness fixed point (IRFP), the problem remains largely open in the case of Majorana fermions which further display a much richer disorder-free phase diagram. Here, pushing the limits of density matrix renormalization group simulations, we carefully examine the ground state of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the noninteracting Majorana IRFP is very stable against finite interactions, in contrast with previous claims.

Arrays of Rydberg atoms have appeared as a remarkably rich playground to study quantum phase transitions in one dimension. One of the biggest puzzles that was brought forward in this context are chiral phase transitions out of density waves. Theoretically predicted chiral transition out of period-four phase is still pending experimental verification mainly due to extremely short interval over which this transition is realized in a single-component Rydberg array. In this Letter, we show that multicomponent Rydberg arrays with extra experimentally tunable parameters provide a mechanism to manipulate quantum critical properties without breaking translation symmetry explicitly. We consider an effective blockade model of two component Rydberg atoms. Weak and strong components obey nearest- and next-nearest-neighbor blockades correspondingly. When laser detuning is applied to either of the two components the system is in the period-3 and period-2 phases. But laser detuning applied to both components simultaneously stabilizes the period-4 phase partly bounded by the chiral transition. We show that relative ratio of the Rabi frequencies of the two components tunes the properties of the conformal Ashkin-Teller point and allows us to manipulate an extent of the chiral transition. The prospects of multicomponent Rydberg arrays in the context of critical fusion is briefly discussed.

We explore critical properties of a chain of interacting Majorana fermions, particles that are their own antiparticles. We study the combined effect of two competing interaction terms of the shortest possible range and show this results in a very rich phase diagram with nine different phases, five of which are critical. In addition, we report a wide variety of quantum phase transitions: the tri-critical Ising lines; the Lifshitz critical line characterized by the dynamical critical exponent z=3; two Kosterlitz-Thouless transitions; and an exotic first-order transition between the floating and the gapped phases. However, the most surprising result is the emergence of the commensurate line at which the floating phases collapse into direct transition. We provide numerical evidences that the resulting multicritical point belongs to the universality class of the eight-vertex model. Implications in the context of supersymmetric properties of the Majorana chain are briefly discussed.

The properties of stable Luttinger liquid phases in models with a nonconserved number of particles are investigated. We study the Luttinger liquid phases in one-dimensional models of hard-core boson and spinless fermion chains where particles can be created and annihilated three by three on adjacent sites. We provide an intuitive and systematic method based on the flow equation approach, which accounts for additional terms in the correlations generated by the Z3-symmetric interactions. We find that despite the emergence of U(1) symmetry under renormalization, the observables are still affected by its breaking in the bare Hamiltonian. In particular, the standard bosonization mapping becomes insufficient to capture the full behavior of correlation functions.

We show that including pairing and repulsion into the description of one-dimensional spinless fermions, as in the domain wall theory of commensurate melting or the interacting Kitaev chain, leads, for strong enough repulsion, to a line of critical points in the eight-vertex universality class terminating floating phases with emergent U(1) symmetry. For nearest-neighbor repulsion and pairing, the variation of the critical exponents along the line that can be extracted from Baxter's exact solution of the XYZ chain at Jx=-Jz is fully confirmed by extensive density matrix renormalization group (DMRG) simulations of the entire phase diagram, and the qualitative features of the phase diagram are shown to be independent of the precise form of the interactions.

We investigate the nature of the phase transitions in the quantum Ashkin-Teller chain in the presence of chiral perturbations. We locate the Lifshitz line separating a region of direct chiral transitions from the region where the transition is through an intermediate floating phase. Furthermore, we identify a small region in the vicinity of the four-state Potts point where chiral perturbations are irrelevant and where the transition remains conformal. Implications to Rydberg atom experiments are briefly discussed.

We study Majorana chain with the shortest possible interaction term and in the presence of hopping alternation. When formulated in terms of spins the model corresponds to the transverse field Ising model with nearest-neighbor transverse and next-nearest-neighbor longitudinal repulsion. The phase diagram obtained with extensive DMRG simulations is very rich and contains six phases. Four gapped phases include paramagnetic, period-2 with broken translation symmetry, Z₂ with broken parity symmetry and the period-2-Z₂ phase with both symmetries broken. In addition there are two floating phases: gapless and critical Luttinger liquid with incommensurate correlations, and with an additional spontaneously broken Z₂ symmetry in one of them. By analyzing an extended phase diagram we demonstrate that, in contrast with a common belief, the Luttinger liquid phase along the self-dual critical line terminates at a weaker interaction strength than the end point of the Ising critical line that we find to be in the tri-critical Ising universality class. We also show that none of these two points is a Lifshitz point terminating the incommensurability. In addition, we analyzed topological properties through Majorana zero modes emergent in the two topological phases, with and without incommensurability. In the weak interaction regime, a self-consistent mean-field treatment provides a remarkable accuracy for the description of the spectral pairing and the parity switches induced by the interaction.

We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possible presence of a critical floating phase at intermediate values of the next-nearest-neighbor interaction. We provide strong evidence that the continuous transition into the dimerized phase, which has been found to be generically in the Wess-Zumino-Witten SU(2)2S universality class up to spin S=2, is SU(2)5 only at two isolated points of the phase diagram, and that it is SU(2)3 in between, in agreement with the presence of two relevant operators allowed by symmetry for SU(2)5, and with the conservation of the parity of the level index along the renormalization flow between SU(2)k theories with different values of k. We also find that the dimerization induced by the next-nearest-neighbor interaction is a three step process, with first a small partially dimerized phase followed by a broad critical floating phase with incommensurate correlations before the fully dimerized phase is reached. Implications for the iron oxide Bi3FeMo2O12 are briefly discussed.

Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with 1/r6 interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with ν≃0.80 for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.