arXiv subjects

Natalia Chepiga

Publications and source records attributed to Natalia Chepiga.

At least 37 records · Page 2Linked to original sources

arXiv2024

Probing universal critical scaling with scan-DMRG

We explore the universal signatures of quantum phase transitions that can be extracted with the density matrix renormalization group (DMRG) algorithm applied to quantum chains with a gradient. We present high-quality data collapses for the order parameter and for the entanglement entropy for three minimal models: transverse-field Ising, 3-state Potts and Ashkin-Teller. Furthermore, we show that scan-DMRG successfully captures the universal critical scaling when applied across the magnetic Wess-Zumino-Witten and non-magnetic Ising transitions in the frustrated Haldane chain. In addition, we report a universal scaling of the lowest excitation energy as a function of a gradient rate. Finally, we argue that the scan-DMRG approach has significantly lower computational cost compare to the conventional DMRG protocols to study quantum phase transitions.

cond-mat.str-el↗

arXiv2024

Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain

We study dimerization transitions in a frustrated spin-3 chain with next-nearest neighbor and three-site interactions. We show that two independent coupling constants of the model are sufficient to fine-tune the system to the critical point in the Wess-Zumino-Witten SU(2)$_6$ universality class. This critical point appears as the end point of an extended SU(2)$_4$ critical line. This implies that the renormalization group flow lead to the critical theory with the largest level $k$ such that the number of relevant operators is reduced by one and the parity of the level is preserved. Furthermore, we argue that due to the presence of marginal operator there is only one point in the SU(2)$_6$ universality class. In addition, we report the appearance of non-magnetic Ising transition between the topologically trivial uniform and dimerized phases. This transition takes place within the singlet sector, while magnetic gap remains open.

cond-mat.str-el↗

arXiv2024

Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling

The experimental realization of the quantum Kibble-Zurek mechanism in arrays of trapped Rydberg atoms has brought the problem of commensurate-incommensurate transition back into the focus of active research. Relying on equilibrium simulations of finite intervals, direct chiral transitions at the boundary of the period-3 and period-4 phases have been predicted. Here, we study how these chiral transitions can be diagnosed experimentally with critical dynamics. We demonstrate that chiral transitions can be distinguished from the floating phases by comparing Kibble-Zurek dynamics on arrays with different numbers of atoms. Furthermore, by sweeping in the opposite direction and keeping track of the order parameter, we identify the location of conformal points. Finally, combining forward and backward sweeps, we extract all critical exponents characterizing the transition.

cond-mat.str-el↗

arXiv2024

Tunable quantum criticality in multicomponent Rydberg arrays

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 multi-component 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 to manipulate an extent of the chiral transition. The prospects of multi-component Rydberg arrays in the context of critical fusion is briefly discussed.

cond-mat.str-el↗

arXiv2023

Emergent U(1) symmetry in non-particle-conserving one-dimensional models

The properties of stable Luttinger liquid phases in models with a non-conserved 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 flow equations approach, which accounts for additional terms in the correlations generated by the $\mathbb{Z}_3$-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.

cond-mat.str-el↗

arXiv2023

Critical properties of the quantum Ashkin-Teller chain with chiral perturbations

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 atoms experiments are briefly discussed.

cond-mat.str-el↗

arXiv2023

Critical properties of the Majorana chain with competing interactions

We study critical properties of a Majorana chain in the presence of two competing interactions of the shortest possible range. The obtained phase diagram is very rich and contains nine different phases, including three floating, two Ising, and four gapped phases. In addition we report a wide variety of quantum phase transitions: the supersymmetric tri-critical Ising lines; the Lifshitz critical line characterized by the dynamical critical exponent $z=3$; Kosterlitz-Thouless transitions, and an exotic first order transition between the floating and the gapped phases. However, the most surprising feature of the obtained phase diagram is the emergence of the commensurate line at which the floating phases collapses into direct transition. We provide numerical evidences that the resulting multi-critical point belongs to the universality class of the eight-vertex model. Implications in the context of supersymmetric properties of the Majorana chain is briefly discussed.

cond-mat.str-el↗

arXiv2023

Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions

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 non-interacting 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 DMRG 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 non-interacting Majorana IRFP is very stable against finite interactions, in contrast with previous claims.

cond-mat.dis-nn↗

arXiv2023

Eight-vertex criticality in the interacting Kitaev chain

We show that including pairing and repulsion into the description of 1D 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 $J_x=-J_z$ is fully confirmed by extensive 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.

cond-mat.str-el↗

arXiv2022

Topological and quantum critical properties of the interacting Majorana chain model

We study Majorana chain with the shortest possible interaction term and in the presence of hoping 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, $\mathbb{Z}_2$ with broken parity symmetry and the $\mathbb{Z}_2$ period-2 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 $\mathbb{Z}_2$ 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.

cond-mat.str-el↗

arXiv2022

Conformal and chiral phase transitions in Rydberg chains

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 $1/r^6$ 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 3-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $ν\simeq 0.80$ 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.

cond-mat.str-el↗

arXiv2022

From Kosterlitz-Thouless to Pokrovsky-Talapov transitions in spinless fermions and spin chains with next-nearest neighbour interactions

We investigate the nature of the quantum phase transition out of charge-density-wave phase in the spinless fermion model with nearest- and next-nearest-neighbor interaction at one-third filling. Using an extensive Density Matrix Renormalization Group (DMRG) simulations we show that the transition changes it nature. We show that for weak next-nearest-neighbor coupling the transition is of Kosterlitz-Thouless type in agreement with bosonisation predictions. We also provide strong numerical evidences that for large next-nearest-neighbor repulsion the transition belongs to the Pokrovsky-Talapov univerality class describing a non-conformal commensurate-incommensurate transition. Finally, we argue that the change of the nature of the transition is a result of incommensurability induced by frustration and realized even at zero doping. The implications in the context of XXZ chain with next-nearest-neighbor Ising interaction is briefly discussed.

cond-mat.str-el↗

arXiv2022

Spinon confinement and deconfinement in spin-1 chains

Motivated by the rich phase diagrams recently unveiled in frustrated spin-1 chains with competing next-nearest neighbour and four-spin interactions, we investigate the nature of the elementary excitations of spin-1 chains in the vicinity of phase transitions using the matrix-product state (MPS) representation of elementary excitations. First, we show that both spinons and magnons naturally arise in SU(2) invariant spin chains when describing ground states and elementary excitations using MPS. Then we investigate the nature of the elementary excitations across the first-oder transition between the Haldane phase and the topologically trivial next-nearest neighbor Haldane phase. We show explicitly that spinons deconfine at the transition, and we calculate the dispersion of these deconfined spinons with MPS. We also show that, immediately away from the transition line, spinons confine, forming dispersive spinon/anti-spinon bound states on both sides of the transition. Finally, we show that deconfined spinons also appear at the transition between the Haldane phase and the spontaneously dimerized phase when this transition is first order.

cond-mat.str-el↗

arXiv2022

From SU(2)$_5$ to SU(2)$_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain

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 ${\mathrm{Bi}}_{3}{\mathrm{FeMo}}_{2}{\mathrm{O}}_{12}$ are briefly discussed.

cond-mat.str-el↗

arXiv2022

Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.

cond-mat.str-el↗

arXiv2021

Supersymmetry and multicriticality in a ladder of constrained fermions

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

cond-mat.str-el↗

arXiv2021

Lifshitz point at commensurate melting of 1D Rydberg atoms

The recent investigation of chains of Rydberg atoms has brought back the problem of commensurate-incommensurate transitions into the focus of current research. In 2D classical systems, or in 1D quantum systems, the commensurate melting of a period-p phase with p larger than 4 is known to take place through an intermediate floating phase where correlations between domain walls or particles decay only as a power law, but when p is equal to 3 or 4, it has been argued by Huse and Fisher that the transition could also be direct and continuous in a non-conformal chiral universality class with a dynamical exponent larger than 1. This is only possible however if the floating phase terminates at a Lifshitz point before reaching the conformal point, a possibility debated since then. Here we argue that this is a generic feature of models where the number of particles is not conserved because the exponent of the floating phase changes along the Pokrovsky-Talapov transition and can thus reach the value at which the floating phase becomes unstable. Furthermore, we show numerically that this scenario is realized in an effective model of the period-3 phase of Rydberg chains in which hard-core bosons are created and annihilated three by three: The Luttinger liquid parameter reaches the critical value $p^2/8=9/8$ along the Pokrovsky-Talapov transition, leading to a Lifshitz point that separates the floating phase from a chiral transition. Implications beyond Rydberg atoms are briefly discussed.

cond-mat.str-el↗

arXiv2020

Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains

Chains of Rydberg atoms have emerged as an amazing playground to study quantum physics in 1D. Playing with inter-atomic distances and laser detuning, one can in particular explore the commensurate-incommensurate transition out of charge-density waves through the Kibble-Zurek mechanism, and the possible presence of a chiral transition with dynamical exponent $z>1$. Here we address this problem theoretically with effective blockade models where the short-distance repulsions are replaced by a constraint of no double occupancy. For the period-4 phase, we show there is an Ashkin-Teller transition point with exponent $ν=0.78$ surrounded by a direct chiral transition with a dynamical exponent $z=1.14$ and a Kibble-Zurek exponent $μ=0.4$. For Rydberg atoms with a van der Waals potential, we suggest that the experimental value $μ=0.25$ is due to a chiral transition with $z\simeq 1.9$ and $ν\simeq 0.47$ surrounding an Ashkin-Teller transition close to the 4-state Potts universality.

cond-mat.str-el↗