Double-weak-link interferometer of hard-core bosons in one dimension

The gist The resulting density profile exhibits clear deviations from the standard Euler-scale hydrodynamic description of the gas, due to genuine quantum interference effects between the two defects.

Introduction and Motivation

The study investigates the dynamics of a lattice hard-core boson gas released from a domain wall initial state in the presence of two weak links (defects) and shows that these defects lead to qualitatively new dynamical behavior that lies beyond the reach of the (generalized) hydrodynamic approach The authors address how the time evolution is modified when multiple defects are present by focusing on a domain wall melting through two conformal defects They find that even at the level of the density profile, the dynamics cannot be captured by a simple hydrodynamic description because quantum-interference effects arising from repeated scattering between the defects play a crucial role.

Single Defect Dynamics

The paper first reviews known results for one conformal defect in Section 2 and derives an exact expression for the propagator in the presence of a single defect. The fermionic propagator Kt(x, y) is derived using the completeness relation in the single-particle eigenbasis of the Hamiltonian Hˆλ, leading to an explicit expression (32) for the propagator. This propagator has a physical interpretation showing that a particle evolves ballistically at velocity v(k) until it hits the defect at position x = 0, where it splits into two wavepackets, one transmitted and one reflected with corresponding transmission/reflection amplitudes √1 − λ2 and λ respectively.

Two Defect Dynamics and Interference

The main focus is on the case of two defects separated by a distance N, where the presence of the second defect modifies the dynamics in a nontrivial way. The system's evolution is described by a set of coupled equations for amplitudes A and B derived from quantization conditions (54), which provide a quantisation condition for k in the form of λ1λ2 = cos(kL) + q1 − λ21q1 − λ22cos(kL − 2kN). The final result for the density profile is given by Eq. (74a), which shows clear deviations from the hydrodynamic prediction, demonstrating that interference effects generated by the two defects persist even at large scales and finite times.

Semiclassical Interpretation and Large-Time Limit

The propagator Kt(x, y) is given by a sum of Bessel functions of the first kind (61), which allows for a semiclassical picture where different terms describe different classical paths. The terms in the propagator describe propagation without defects, propagation with one reflection at position 1, and paths involving multiple reflections between the two defects. In the large-time limit where N/t → 0, the dynamics become classical again and one can write down an evolution equation for the Wigner function in a form of Eq. (76). In this regime, the two defects can be effectively treated as a single composite defect because interference effects are progressively washed out by the large number of contributing paths.

Conclusion and Significance

The work demonstrates that the Euler-scale dynamics differ markedly from the predictions of the generalized hydrodynamics description, with this breakdown originating from quantum-interference effects generated by repeated scattering processes between the defects. By deriving these propagators explicitly, the authors showed that a meaningful semiclassical description can still be recovered provided that the scattering picture accounts for coherent multiple reflections. This extends the approach previously developed for systems containing a single conformal defect and suggests that the method generalizes to higher numbers of defects and to more general (i.e. non-conformal) defects. The results provide a comprehensive and fully controlled description of the dynamics, firmly establishing the role of interference effects beyond conventional hydrodynamics.

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Attila Takacs ´ Jer´ ome Dubail Pasquale Calabrese April 1, 2026 Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia Universite de Lorraine, CNRS, LPCT, F-54000 Nancy, France CESQ and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France SISSA and INFN, Via Bonomea 265, 34136 Trieste, Italy Abstract We study the dynamics of a lattice hard-core boson gas released from a domain wall initial state in the presence of two weak links (defects) when the two defects are separated by a finite distance, the resulting density profile exhibits clear deviations from the standard Euler-scale hydrodynamic description of the gas due to genuine quantum interference effects between the two defects By analyzing the exact fermionic propagators, we show that repeated reflections at the defects give rise to interference fringes and coherent patterns that are beyond the reach of the (generalized) hydrodynamic description. We derive a closed analytic expression for the density profile during the expansion, explicitly highlighting the role played by these interference processes. 1 Introduction Over the past decade, remarkable progress has been achieved in understanding the dynamics of integrable one-dimensional quantum gases, largely driven by Generalized Hydrodynamics (GHD) [1, 2] One way to interpret the GHD theory is to regard it as an emergent classical equation for quasi-particles that propagate ballistically through the system [1–8] This picture applies to a wide variety of physical situations and provides a powerful framework to understand also more complex phenomena such as diffusion [7, 8], dissipation [9, 10] One interesting physical situation that has remained relatively unexplored within the framework of GHD is that of localised impurities or defects The study of impurities has a very rich history in one-dimensional quantum physics, dating back to the Anderson orthogonality catastrophe [11] and the Kane-Fisher model [12] In the latter, a renormalization-group analysis reveals that transport through an impurity in a Luttinger liquid is qualitatively different depending on whether the interactions are attractive or repulsive The out-of-equilibrium description of such systems, however, remains comparatively less developed.

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Hard-core bosons on a line with a single defect 2.1 Hard-core bosons and hydrodynamics of free fermions: no defect We consider a gas of hard-core bosons hopping on a one-dimensional lattice, described by the Hamiltonian Hˆ = − 1/2 X x∈Z (ˆσ+x σˆ−x+1 + ˆσ+x+1σ−x) (1) where σˆ+x(σˆ−x) is the Pauli operator that creates (destroys) a hard-core boson on site x. The model has nearest-neighbour hopping, and here we do not consider defects that will be introduced in the next subsection In spin language, the Hamiltonian (1) is that of the XX spin chain It is well-known that, under the Jordan-Wigner mapping σˆ+x = e iπ Px−1 j=−∞ cˆ†j cˆj cˆ†x, σˆ−x = e −iπ Px-1 j=−∞ cˆ†j cˆj ĉ x (2) where ĉ† x, ĉ x are fermion creation/annihilation operators that obey the canonical anti-commutation relations

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2. Hard-core bosons on a line with a single defect 2.2 Hard-core bosons with a defect The dynamics of lattice hard-core bosons or free fermions with a single defect was investigated in previous works [19, 32, 33] In particular, an emergent quasi-particle picture was derived, which allows the calculation of the density profile and other quantities such as the bipartite entanglement entropy to leading order in time. The model considered in Ref.

1. Bold header: Generalized Hydrodynamics (GHD) Integration

The improved AI system can accurately model out-of-equilibrium dynamics by incorporating genuine quantum interference effects between the two defects which are described as being beyond the reach of the (generalized) hydrodynamic description. This allows the system to predict density profiles that deviate from standard Euler-scale descriptions.

2. Bold header: Exact Propagator Calculation

The system can derive and utilize exact fermionic propagators, such as Eq. (32) for a single defect and Eq. (61) for two defects, which are explicitly beyond the reach of the (generalized) hydrodynamic description. This enables the AI to calculate density profiles that are benchmarked against numerics with perfect agreement.

3. Bold header: Semiclassical Path Interpretation

The system can interpret complex dynamics by performing a semiclassical picture, where terms in the propagators describe specific classical paths, such as one term representing a path without being affected by either of the defects, and another describing a path with a reflection at position 1.