{"id":"8e77db07-9eed-4f41-b6a6-e651324136e9","arxiv_id":"2508.19406","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For a local joining quench, the entanglement Hamiltonian of a finite free-fermion chain is local in the continuum limit, with distinct left/right-moving inverse temperatures, matching exact numerics.","lead":"This paper derives the time-dependent entanglement Hamiltonian for a 1D free-fermion chain after two half-chains are suddenly joined, finding a local expression with different weights for left- and right-moving energy. It then shows that exact lattice calculations match this conformal field theory prediction once a proper continuum limit is taken.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified; the branch-choice step in Appendix A is delicate but independently supported by the lattice sums.","rationale":"The paper's central claim is well supported. The CFT derivation follows the established Cardy-Tonni framework, the entropy calculation reproduces the known result of Refs. [7,46], and the lattice continuum-limit procedure has no free parameters. The numerical comparison in Figs. 4 and 5 is non-trivial: the sums in Eq. (41) are independent of the CFT branch discussion and nonetheless match the predicted β0 and β1, including the piecewise structure of the decentered case. I therefore do not see a live flaw that would overturn the reader's ACCEPT verdict. The branch-choice issue flagged by the reader is indeed the most delicate theoretical step, but it is already mitigated by independent numerical evidence, and the proposed continuation test would settle it definitively. The observed oscillations near x=t and near the boundary are acknowledged by the authors and appear to be finite-size effects; they do not undermine the qualitative and quantitative agreement of the weights. Hence the verdict should remain UNCHANGED.","tokens_in":17491,"tokens_out":19399,"duration_ms":227468,"concrete_test":"Numerically implement the conformal map (14) with a small but nonzero λ, starting at τ=0+ where ξ(iτ)=i, and continue τ along the straight path to τ=it for fixed x and x0, choosing the square-root branch by continuity. Evaluate β(z) from Eq. (20) and compare the resulting β(x,t) and β̄(x,t) with the piecewise expressions in Eq. (29) for t<x0, x0<t<x, and x0<x<t. If the numerical continuation reproduces (29) in all regimes, the branch choice is validated; if it yields different signs, Eq. (29) would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most delicate step in the CFT derivation is the resolution of the square-root branch in ξ(z) after the Wick rotation τ→it, which controls the piecewise form of β(x,t) and β̄(x,t) in Eq. (29). A different, still locally consistent branch prescription would change the predicted weights and hence the central claim. However, this concern does not currently land: the lattice continuum-limit sums in Eq. (41) are derived directly from the EH matrix and contain no input about the CFT branch choice, yet they reproduce the piecewise CFT curves in Fig. 5 across all three time regimes (t<x0, x0<t<x, and x0<x<t). The same branch choice is also consistent with the known infinite-chain limit (28), with continuity of β at x=x0 and x=t, and with the entropy result (33). The visible oscillations near the front and boundary are acknowledged finite-size/lattice artifacts and do not affect the qualitative agreement. Still, because the UHP prescription in Appendix A is imposed rather than derived from an explicit continuation path, a direct check would remove residual doubt.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper investigates the entanglement Hamiltonian (EH) after a local joining quench in a finite chain of free fermions. The authors first generalize the Cardy–Tonni CFT approach to a finite geometry with open boundaries. They map the double-pants geometry to an annulus and derive the EH as a weighted integral of the right- and left-moving stress-tensor components. For the half-chain partition (x0=0) they obtain explicit weights β(x,t) and β̄(x,t) in Eq. (27); for a decentered subsystem (x0>0) they obtain piecewise expressions in Eq. (29). They also compute the entanglement entropy from these weights and recover the known result of Stephan and Dubail. On the lattice side, they compute the exact EH matrix via the correlation-matrix method and develop a continuum limit of the lattice EH in terms of sums over hopping amplitudes (Eqs. 40–41). For the half-filling case, these sums simplify and yield the weights β0 and β1, which are compared to the CFT prediction through Eq. (42). Exact numerical data for L=100 show good agreement for various times and both subsystem geometries, with only small oscillations near the front and boundary.","tokens_in":17767,"tokens_out":22378,"duration_ms":217024,"significance":"This is a significant result in the study of entanglement Hamiltonians in non-equilibrium systems. It provides, to my knowledge, the first explicit CFT prediction for the local EH after a local quench in a finite system and its verification by exact lattice numerics. The CFT derivation is parameter-free, and the lattice calculation is independent, so the agreement is highly nontrivial. The result contrasts with the global quench case, where the lattice EH is genuinely long-range, and shows that for a local low-energy quench the continuum EH remains local. The paper is well organized, with detailed appendices that make the calculations reproducible. The numerical evidence is strong, and the limitations (oscillations, slow convergence of the sums) are honestly acknowledged.","major_comments":[],"minor_comments":[{"comment":"The branch-choice prescription (requiring ξ(z) and ξ0 to lie in the UHP after analytic continuation) is stated but not derived. Since the piecewise form of β(x,t) and β̄(x,t) is a central result, a brief justification of why this prescription follows from a consistent continuation path—or an explicit statement that it is a working assumption supported by the lattice checks—would remove residual ambiguity.","section":"Appendix A / Eq. (29)"},{"comment":"The convergence of the sums in the continuum limit is only empirical. The paper notes that the decay in p is slow, especially for s_{2p}(x). Adding a plot for different lattice sizes (e.g., L=50, 100, 200) or a short discussion of the asymptotic behavior would strengthen the continuum-limit claim.","section":"Section IV / Eq. (41)"},{"comment":"The oscillations for j>t are mentioned but not quantified. A comment on their scaling with L or their relation to finite-size effects (e.g., the front width) would be useful for the reader to judge the discrepancy.","section":"Fig. 4"},{"comment":"The regularization A_{ε,λ} assumes t < L−λ; for t close to L the second interval [t+λ, L] is empty and Eq. (31) should be adjusted or the regime of validity stated. This is a minor technical point, but it would improve the rigor of the entropy check.","section":"Section III.C / Eq. (31)"},{"comment":"The L→∞ limit is said to reproduce the result of [7], which is a general review. Consider also citing the original local-quench entropy papers (e.g., [45,46]) at this point for historical accuracy.","section":"References / Eq. (28)"}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid contribution and the numerical evidence is convincing. The branch-choice and convergence concerns are minor and should be addressable without new calculations. The work is within the scope of the journal, and I recommend acceptance after minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the Bonsignori–Eisler paper. Bottom line: the main claim holds. They generalize Cardy–Tonni to the finite-L joining quench, get explicit chiral weights beta and betabar (eqs 27,29), and then show the lattice EH for free fermions, after the appropriate continuum limit, reproduces those weights. The continuum limit involves imaginary hopping terms, which is genuinely new for this quench, and the matching is convincing, not tuned. The L→∞ limit reduces to [7] and the entanglement entropy reproduces [46]; both are good consistency checks.\n\nCredit where due: the derivation follows the established conformal mapping, with real extra work in the branch-choice appendix. The lattice numerics are exact, and the sums in (41) contain no input from the CFT branch choice, so the agreement in Figs. 4 and 5 is real evidence, not a fit. The parity structure t_{2p}=0, s_{2p+1}=0 is a nice simplification that removes the chemical potential and current terms.\n\nSoft spots, in proportion: the oscillations for j>t are visible, stronger at early times, and the paper calls the agreement 'remarkable' without quantifying them. That is a minor complaint; the overall shape is clearly right. The convergence of the diagonal sums in (41) is empirical—they say you essentially need the complete sum, especially for s_{2p}—but they do not provide a convergence test or error estimates. A referee should ask for that. The branch-choice step in Appendix A is the delicate one: they fix signs so that xi and xi0 sit in the UHP after analytic continuation. This is imposed, not derived from an explicit continuation path. The stress-test concern about it does not land, because the lattice sums are independent of that choice and reproduce the piecewise beta, but a referee should push for a cleaner justification or a direct numeric check of the continuation.\n\nWho this is for: people working on entanglement Hamiltonians in CFT and lattice models, local quench dynamics, modular Hamiltonians. It does not claim broader technology, and it does not need to. It deserves a serious referee; I would send it to review. If I were editing, I would not desk-reject it.","headline":"Solid paper: finite-L CFT weights for joining-quench EH, plus a lattice continuum limit that nails the prediction; worth refereeing.","tokens_in":18146,"tokens_out":1504,"would_cite":true,"duration_ms":17739,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"After a joining quench, the entanglement Hamiltonian stays local in the continuum, with right- and left-movers carrying different weights.","keywords":["entanglement Hamiltonian","local quench","conformal field theory","free fermions","continuum limit","modular Hamiltonian","entanglement entropy","joining quench"],"falsifier":"Compute the continuum-limit weights from (41) for a subsystem displaced from the quench (x0 > 0) at times just after the front arrives (t slightly larger than x0): the prediction (29) has β and β̄ given by different piecewise formulas on the two sides of x = t, so the ratio β1/β0 should jump exactly at j = t. If the numerical ratio crosses smoothly or at the wrong location, the branch-cut choice in Appendix A is wrong.","tokens_in":17446,"feed_emoji":"⚛️","tokens_out":8507,"duration_ms":86482,"temperature":0.7,"pith_summary":"Two independent half-chains of free fermions, each in its ground state, are suddenly joined at their ends. This paper shows that, in the continuum limit described by conformal field theory, the entanglement Hamiltonian of a subsystem is a local operator: an integral of the energy density with two distinct weight functions, one for right-moving and one for left-moving modes. The weights have zeros at the entangling point and at the ballistic front created by the quench, and their structure explains why right-movers contribute three times as much to the entanglement entropy as left-movers. Exact numerics on a hopping chain, after summing away the lattice's long-range hopping tails, reproduce these weights. The result contrasts with the global quench, where the lattice entanglement Hamiltonian stays genuinely long-range.","feed_headline":"A joining quench keeps the entanglement Hamiltonian local","feed_subtitle":"Two local inverse temperatures, one per light-cone direction, match exact lattice data once hopping tails are summed away.","key_machinery":"The conformal map from the 'double-pants' geometry of the quench path integral to an annulus, ξ(z) = i√[sin(π(iλ+z)/2L)/sin(π(iλ−z)/2L)], followed by the logarithmic map w = log ζ. In the strip geometry the entanglement Hamiltonian is a translation generator, and the inverse-temperature weights follow from β = 2π/w′(z); analytic continuation τ→it turns them into the piecewise functions in (27) and (29). On the lattice side, the carrying mechanism is the continuum limit of the EH hopping matrix: substituting c_j → √a(e^{ik_F x}ψ + e^{−ik_F x}ψ̄) and summing the diagonals t_r, s_r gives β0 and β1 via (41), which at half filling decouples into purely real and imaginary diagonals and kills the p","core_discovery":"On the paper's own terms, the central discovery is an explicit local CFT prediction for the entanglement Hamiltonian after a joining quench on a finite chain of 2L sites: H = ∫A dx [β(x,t) T(x−t) + β̄(x,t) T̄(x+t)], with piecewise trigonometric weights. For a subsystem starting at the junction (x0 = 0) the weights are β = 4L |sin(πx/2L) sin(π(x−t)/2L) / sin(πt/2L)| and β̄ with x+t, valid for λ→0, t≫λ; for an arbitrary partition x0 > 0, the branch cuts of the conformal map force three different regimes, giving the piecewise expression in (29). The lattice calculation shows that the EH matrix contains long-range real and imaginary hopping terms, but the properly defined continuum limit—summing","pith_inferences":["One natural next test is away from half filling: the CFT weights should simply rescale time by the Fermi velocity, while the lattice sums in (40) lose the even/odd diagonal separation; comparing the two would isolate whether the continuum limit still converges.","The local form suggests an experimental target the paper leaves implicit: in a cold-atom or ion realization of the joining quench, one could reconstruct ρA and look for the two inverse-temperature profiles, with the zero of β0 at the moving front as a direct signature.","The strong lattice oscillations seen for small t near the unvisited region raise a testable question: do they vanish in the L→∞ limit at fixed t, or does the continuum limit require t large enough that the front has spread? Numerics at larger L would settle it."],"forward_implications":["The EH is local in the continuum: a weighted integral of T00 and T01, so a local-temperature interpretation is valid for this out-of-equilibrium protocol.","The right-moving front acts as a moving entangling point inside the subsystem, which is why right-movers contribute three times the left-movers to the entropy; the total entropy matches the known CFT result S = (c/3) log[(2L/π)√(λϵ) sin(πt/2L)].","After the front reflects from the boundary at t = L, the weights satisfy β(x, 2L − t) = β̄(x, t), so the late-time EH is obtained by exchanging chiralities.","On the lattice, convergence to the CFT result requires the full sum over diagonals of the EH matrix; the first diagonal alone is not enough, especially for the imaginary (current) part.","The weight behind the front is time-independent (β0 = 2 sin πx for the half-chain), and at t = L the momentum-density weight β1 vanishes; both features are visible in the L = 100 numerics."],"supporting_citations":[{"why":"Supplies the CFT technique of mapping the entanglement Hamiltonian to an annulus/strip and the formula β = 2π/w′ used throughout.","marker":"[14]"},{"why":"Provides the double-pants path-integral construction and the entanglement-entropy result that the derived weights reproduce.","marker":"[46]"},{"why":"Gives the continuum-limit procedure for lattice entanglement Hamiltonians that the numerical comparison relies on.","marker":"[26]"},{"why":"Earlier lattice study of the joining quench that observed the propagating front in correlation eigenvectors, used as the lattice counterpart to the CFT front.","marker":"[38]"},{"why":"Supplies the ground-state correlation matrix of an open half-chain used as the initial state.","marker":"[55]"},{"why":"Gives the infinite-chain CFT treatment whose L→∞ limit the derived weights reduce to in (28).","marker":"[7]"},{"why":"Provides the exact relation H = ln[(1−C)/C] that converts the reduced correlation matrix into the lattice EH matrix.","marker":"[56]"},{"why":"Shows that for a global quench the lattice EH remains long-range, providing the contrast that motivates the continuum-limit comparison here.","marker":"[36]"}],"fun_headline_variants":["Joining quench yields local entanglement Hamiltonian","Two inverse temperatures emerge after local quench","Local entanglement Hamiltonian after joining quench","CFT matches lattice for post-quench entanglement","Entanglement Hamiltonian stays local in joining quench"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The derivation depends on fixing the sign of a square root in the conformal map so that the relevant image points lie in the upper half-plane after continuing τ→it; a different branch choice changes the piecewise weights and the entropy.","fun_headline_variants_meta":{"raw":{"variants":["Joining quench yields local entanglement Hamiltonian","Two inverse temperatures emerge after local quench","Local entanglement Hamiltonian after joining quench","CFT matches lattice for post-quench entanglement","Entanglement Hamiltonian stays local in joining quench"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000151,"raw_usage":{"total_tokens":989,"prompt_tokens":651,"completion_tokens":338,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":395,"completion_tokens_details":{"reasoning_tokens":271}},"tokens_in":395,"tokens_out":338,"duration_ms":3747,"temperature":1.0,"reasoning_tokens":271,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T15:46:49.382528+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the continuum-limit weights from (41) for a subsystem displaced from the quench (x0 > 0) at times just after the front arrives (t slightly larger than x0): the prediction (29) has β and β̄ given by different piecewise formulas on the two sides of x = t, so the ratio β1/β0 should jump exactly at j = t. If the numerical ratio crosses smoothly or at the wrong location, the branch-cut choice in Appendix A is wrong.","supporting_citations":[{"cited_title":"Cardy and E","cited_arxiv_id":null,"evidence_quote":"Supplies the CFT technique of mapping the entanglement Hamiltonian to an annulus/strip and the formula β = 2π/w′ used throughout."},{"cited_title":"St´ ephan and J","cited_arxiv_id":null,"evidence_quote":"Provides the double-pants path-integral construction and the entanglement-entropy result that the derived weights reproduce."},{"cited_title":"Eisler, E","cited_arxiv_id":null,"evidence_quote":"Gives the continuum-limit procedure for lattice entanglement Hamiltonians that the numerical comparison relies on."},{"cited_title":"Eisler and I","cited_arxiv_id":null,"evidence_quote":"Earlier lattice study of the joining quench that observed the propagating front in correlation eigenvectors, used as the lattice counterpart to the CFT front."},{"cited_title":"Fagotti and P","cited_arxiv_id":null,"evidence_quote":"Supplies the ground-state correlation matrix of an open half-chain used as the initial state."},{"cited_title":"Calabrese and J","cited_arxiv_id":null,"evidence_quote":"Gives the infinite-chain CFT treatment whose L→∞ limit the derived weights reduce to in (28)."},{"cited_title":"Peschel, Calculation of reduced density matrices from correlation functions, J","cited_arxiv_id":null,"evidence_quote":"Provides the exact relation H = ln[(1−C)/C] that converts the reduced correlation matrix into the lattice EH matrix."},{"cited_title":"Rottoli, C","cited_arxiv_id":null,"evidence_quote":"Shows that for a global quench the lattice EH remains long-range, providing the contrast that motivates the continuum-limit comparison here."}],"review_version":1}